Magnetic Variation Calculator

Calculate the angular difference between magnetic north and true north for any location and date with precision.

Introduction & Importance of Magnetic Variation

Understanding the critical difference between true north and magnetic north

Magnetic variation (also called magnetic declination) represents the angle between magnetic north (the direction the north end of a compass needle points) and true north (the direction along a meridian toward the geographic North Pole). This angular difference is not constant but varies depending on both location and time due to changes in Earth’s magnetic field.

The importance of magnetic variation cannot be overstated for:

• Aviation: Pilots must account for magnetic variation when navigating using compass headings to ensure accurate flight paths. The Federal Aviation Administration (FAA) requires magnetic variation corrections for all flight planning.
• Maritime Navigation: Ships rely on magnetic compasses for primary navigation, with variations of even 1° potentially causing significant course deviations over long distances.
• Land Surveying: Professional surveyors must apply magnetic variation corrections to ensure property boundaries and topographic maps maintain legal accuracy.
• Military Operations: All branches of the military use magnetic variation data for artillery targeting, aerial operations, and ground navigation.
• Outdoor Recreation: Hikers, orienteers, and wilderness explorers depend on accurate declination adjustments for safe navigation in remote areas.

The Earth’s magnetic field is generated by the motion of molten iron in its outer core, creating a complex, dynamic system that changes continuously. The World Magnetic Model (WMM), produced by the National Oceanic and Atmospheric Administration (NOAA) and the British Geological Survey, provides the most authoritative data for calculating magnetic variation worldwide.

How to Use This Magnetic Variation Calculator

Step-by-step guide to obtaining accurate declination values

1. Enter Your Location:
   • Input latitude in decimal degrees (negative for southern hemisphere). Example: 40.7128 for New York City
   • Input longitude in decimal degrees (negative for western hemisphere). Example: -74.0060 for New York City
   • For maximum precision, use coordinates with at least 4 decimal places
2. Select the Date:
   • Choose the specific date for which you need the magnetic variation
   • The calculator accounts for the annual change in declination (typically 0.1° to 0.3° per year)
   • For historical data, select past dates; for future planning, select upcoming dates
3. Specify Altitude (Optional):
   • Enter your elevation above sea level in meters
   • Altitude affects magnetic field strength but has minimal impact on declination for most practical purposes
   • Default value of 0 meters (sea level) is appropriate for most applications
4. Calculate and Interpret Results:
   • Click “Calculate Magnetic Variation” to process your inputs
   • The results will display:
     • Magnetic Declination: The angle between true north and magnetic north (positive for east, negative for west)
     • Annual Change: How much the declination changes each year at your location
     • Grid Variation: The difference between grid north and magnetic north (important for topographic maps)
   • The interactive chart visualizes how declination has changed at your location over time
5. Applying the Results:
   • For compass navigation: Add easterly variation or subtract westerly variation from true bearings
   • For map work: Use the grid variation to convert between grid bearings and magnetic bearings
   • For aviation: Apply the variation to convert between true headings and magnetic headings

Pro Tip: For critical navigation applications, always verify your calculated variation against the most recent NOAA Magnetic Field Calculator and cross-reference with current aeronautical charts or nautical publications.

Formula & Methodology Behind the Calculator

The scientific foundation of magnetic variation calculations

Our calculator implements the World Magnetic Model (WMM) 2020, which is the standard model used by NATO, the U.S. Department of Defense, the UK Ministry of Defence, and the International Hydrographic Organization. The model provides a mathematical representation of Earth’s main magnetic field and its secular variation (time-dependent changes).

Core Mathematical Components

The WMM represents the magnetic potential (V) as a series expansion of spherical harmonics:

V(r,θ,φ) = a ∑n=1N (a/r)n+1 ∑m=0n [gnm cos(mφ) + hnm sin(mφ)] Pnm(cosθ)

Where:

• r, θ, φ: Spherical coordinates (geocentric radius, colatitude, longitude)
• a: Reference radius (6371.2 km)
• g_n^m, h_n^m: Gauss coefficients (updated every 5 years)
• P_n^m: Associated Legendre functions
• N: Maximum degree of the expansion (12 for WMM2020)

The magnetic declination (D) is then calculated from the horizontal components of the magnetic field (X and Y):

D = atan2(Y, X)

Secular Variation Implementation

The WMM includes time-dependent terms to account for the changing magnetic field:

gnm(t) = gnm(t0) + ṡnm × (t - t0)

Where ṡ_n^m represents the secular variation coefficients, and t₀ is the base epoch (2020.0 for WMM2020).

Validation and Accuracy

The WMM2020 has the following accuracy specifications:

• Declination (D): ±0.5° at sea level, increasing to ±1° at high altitudes
• Annual Change: ±0.1°/year
• Validity Period: 2020-2025 (with annual updates for secular variation)

For locations near the magnetic poles or at high altitudes (>1000km), specialized models like the International Geomagnetic Reference Field (IGRF) may provide better accuracy.

Real-World Examples & Case Studies

Practical applications of magnetic variation calculations

Case Study 1: Transatlantic Flight Planning

Scenario: Commercial airline flight from New York JFK (40.64°N, 73.78°W) to London Heathrow (51.47°N, 0.45°W) on June 15, 2023

Calculation:

• JFK Magnetic Variation: -13.3° (13° 18′ West)
• Heathrow Magnetic Variation: -1.8° (1° 48′ West)
• Annual Change: +0.05°/year at JFK, +0.18°/year at Heathrow

Application: The flight plan must account for these variations when converting between true tracks and magnetic headings. The 11.5° difference between departure and arrival variations requires careful waypoint planning to maintain accurate navigation throughout the flight.

Impact: Without proper variation correction, a 1° error over a 3,000 nautical mile flight would result in a lateral deviation of approximately 52 nautical miles at the destination.

Case Study 2: Offshore Oil Platform Positioning

Scenario: Positioning a drilling platform in the Gulf of Mexico (27.5°N, 95.0°W) with required accuracy of ±5 meters

Calculation:

• Magnetic Variation: 4.2° East (2023 value)
• Annual Change: -0.08°/year
• Grid Convergence: 0.3° (UTM Zone 15N)

Application: Surveyors must apply both magnetic variation and grid convergence corrections when:

• Establishing primary control points using GPS
• Laying out the platform foundation relative to true north
• Verifying compass-based measurements from support vessels

Impact: A 1° error in variation would result in a positional error of 17.5 meters per kilometer of distance measured, potentially causing costly misalignments in the multi-billion dollar infrastructure.

Case Study 3: Wilderness Search and Rescue

Scenario: Search team in Denali National Park (63.0°N, 151.0°W) at 2,000m elevation, using compass and topographic map

Calculation:

• Magnetic Variation: 18.5° East (2023 value)
• Annual Change: -0.22°/year
• Grid Variation: 2.1° (UTM Zone 6N)

Application: Team must:

• Add 18.5° to all map bearings to get magnetic bearings
• Account for the 2.1° grid convergence when using UTM coordinates
• Adjust for the significant annual change if using older maps

Impact: In this extreme environment, a 2° error could result in missing a 1km-wide search area after traveling just 15km, with potentially life-threatening consequences.

Data & Statistics: Magnetic Variation Trends

Comprehensive analysis of global magnetic field changes

Global Magnetic Variation Extremes (2023 Data)

Location	Latitude	Longitude	Magnetic Variation	Annual Change	Notes
North Magnetic Pole	86.50°N	164.00°E	180.0° (undefined)	+50.0°/year	Pole moving rapidly toward Siberia at ~50km/year
South Magnetic Pole	64.00°S	135.00°E	0.0° (undefined)	+10.0°/year	Moving northwest at ~10-15km/year
New York City, USA	40.71°N	74.00°W	-13.3°	+0.05°/year	Westerly variation decreasing slowly
London, UK	51.50°N	0.12°W	-1.8°	+0.18°/year	Near zero variation with moderate change
Sydney, Australia	33.87°S	151.21°E	12.1°	+0.10°/year	Easterly variation increasing gradually
Tokyo, Japan	35.68°N	139.76°E	-7.5°	+0.08°/year	Westerly variation decreasing slowly
Cape Town, South Africa	33.92°S	18.42°E	-24.8°	+0.20°/year	Large westerly variation with significant change

Historical Variation Changes in Major Cities

City	1900	1950	2000	2020	2023	Change (1900-2023)
Washington D.C., USA	-8.0°	-10.5°	-11.0°	-10.8°	-10.5°	-2.5°
Paris, France	-12.0°	-6.0°	-2.0°	-0.5°	+0.2°	+12.2°
Moscow, Russia	+8.5°	+10.0°	+11.5°	+12.5°	+12.8°	+4.3°
Beijing, China	-4.5°	-5.0°	-5.8°	-6.0°	-6.1°	-1.6°
Rio de Janeiro, Brazil	-20.0°	-21.5°	-22.0°	-21.8°	-21.6°	-1.6°
Melbourne, Australia	+9.5°	+10.5°	+11.5°	+12.0°	+12.2°	+2.7°

The data reveals several important trends:

1. Pole Movement: The North Magnetic Pole has moved from northern Canada toward Siberia at an accelerating rate, increasing from ~10km/year in the 1990s to ~50km/year currently.
2. Regional Differences: Western Europe has seen the most dramatic changes (Paris changed by 12.2° in 123 years), while some regions like Beijing show relatively stable variations.
3. Acceleration: The rate of change has increased in recent decades, with the 2020 WMM requiring an unprecedented early update in 2019 due to rapid magnetic field shifts.
4. Local Anomalies: Areas like Cape Town experience both large variations (-24.8°) and significant annual changes (+0.20°/year), requiring frequent updates to navigation systems.

For the most current magnetic field data, consult the NOAA Geomagnetism Program or the British Geological Survey.

Expert Tips for Working with Magnetic Variation

Professional advice for accurate navigation and measurement

Compass Adjustment

1. Mechanical Compasses: Most quality compasses (Suunto, Silva, Brunton) have adjustable declination screws. Set this to your calculated variation for direct map-to-field readings.
2. Digital Compasses: Devices like Garmin GPS units allow electronic declination adjustment. Update this setting whenever you change locations significantly.
3. Verification: Always verify your compass adjustment by:
   • Comparing with a known bearing (like a surveyed property line)
   • Using the “sun shadow” method at solar noon
   • Cross-checking with GPS bearings (remember GPS uses true north)

Map Work Techniques

• Conversion Formulas:
  • True Bearing = Magnetic Bearing + Easterly Variation
  • True Bearing = Magnetic Bearing – Westerly Variation
  • Grid Bearing = True Bearing – Grid Convergence
• Protractor Use: When measuring bearings on maps:
  • Always use the map’s declination diagram as a secondary check
  • For UTM grids, remember convergence increases with distance from the central meridian
  • Use a 1:50,000 scale map or better for precise work
• Temporal Adjustments: For old maps:
  • Calculate the variation change: ΔD = annual_change × (current_year – map_year)
  • Apply the adjustment: current_variation = map_variation + ΔD

Advanced Applications

• Aerial Photography:
  • Apply variation corrections when georeferencing oblique aerial images
  • Use the calculated variation to orient flight lines perpendicular to the sun’s azimuth for optimal lighting
• Marine Navigation:
  • For celestial navigation, convert between magnetic and true bearings when using sextant sights
  • Account for variation changes when plotting DR (dead reckoning) positions over long voyages
• Geophysical Surveying:
  • Apply diurnal variation corrections for high-precision magnetic surveys
  • Use the WMM to remove the main field when analyzing magnetic anomalies
• Drone Operations:
  • Program autonomous drones with the correct local variation for accurate waypoint navigation
  • Update variation settings seasonally for long-term mapping projects

Common Pitfalls to Avoid

1. Ignoring Annual Change: Using outdated variation data can introduce errors of several degrees over time. Always calculate for your specific date.
2. Mixing Datums: Don’t confuse magnetic variation with grid convergence. They serve different purposes and have different values.
3. Local Anomalies: Areas with magnetic ore deposits can have local variations that differ significantly from the regional model. Always verify with local surveys when possible.
4. High Latitude Errors: The WMM becomes less accurate near the magnetic poles. For polar operations, use specialized models like the IGRF.
5. Altitude Effects: While our calculator includes altitude, most recreational applications can ignore this parameter as the effect is minimal below 10,000 meters.
6. Compass Interference: Even with perfect variation data, metal objects or electronic devices can deflect compass needles. Always check for interference.

Interactive FAQ: Magnetic Variation Questions

Expert answers to common questions about magnetic declination

Why does magnetic variation change over time?

Magnetic variation changes because Earth’s magnetic field is generated by the complex motion of molten iron and nickel in the outer core, approximately 2,900 km below the surface. This fluid motion creates electric currents through the dynamo effect, which in turn generate the magnetic field.

Several factors contribute to the temporal changes:

1. Core Dynamics: Turbulent convection in the outer core causes continuous changes in the magnetic field’s strength and orientation.
2. Secular Variation: Long-term trends (decades to centuries) caused by slow changes in core flows. The North Magnetic Pole, for example, has moved from Canada toward Siberia at an accelerating rate.
3. Geomagnetic Jerks: Abrupt changes in the rate of secular variation that occur approximately every 1-12 years. The most recent significant jerk occurred in 2016.
4. Solar Influence: While the 11-year solar cycle has minimal direct effect on declination, solar storms can cause short-term magnetic disturbances.

The World Magnetic Model is updated every 5 years to account for these changes, with the current WMM2020 valid through 2025. Our calculator automatically applies the appropriate secular variation corrections based on your selected date.

How often should I update my magnetic variation data?

The update frequency depends on your application and location:

Application	Recommended Update Frequency	Critical Threshold
General Recreation (hiking, orienteering)	Every 2-3 years	±1° change from last update
Professional Surveying	Annually	±0.5° or 1 year since last update
Aviation (VFR)	Every 6 months	±0.3° or as per FAA NOTAMs
Maritime Navigation	Quarterly	±0.2° or as per nautical charts
Military Operations	Monthly	Per operational requirements
Polar Regions	Real-time updates	Specialized models required

For most users, we recommend:

• Check variation before any critical navigation task
• Update your compass adjustment at the start of each outdoor season
• Verify against current aeronautical charts or nautical publications for aviation/marine use
• Use our calculator to check how much the variation has changed since your last update

Remember that the rate of change varies by location. Areas near the magnetic poles or along the agonic line (0° variation) can experience more rapid changes.

What’s the difference between magnetic variation and grid convergence?

While both magnetic variation and grid convergence represent angular differences from true north, they arise from completely different phenomena and serve different purposes:

Magnetic Variation

• Definition: Angle between magnetic north and true north
• Cause: Earth’s magnetic field orientation
• Changes With: Location and time
• Typical Values: -30° to +30° (extremes near poles)
• Measurement: Determined by magnetic field models (WMM)
• Use: Compass navigation, aviation headings

Grid Convergence

• Definition: Angle between grid north and true north
• Cause: Map projection distortion (UTM, state plane)
• Changes With: Only location (constant over time)
• Typical Values: -3° to +3° (increases with distance from central meridian)
• Measurement: Calculated from map projection parameters
• Use: Topographic map work, surveying

Key Relationship: Grid Magnetic Angle (GMA) = Grid Convergence – Magnetic Variation

This relationship allows conversion between grid bearings and magnetic bearings, which is essential when working with topographic maps that use grid north as their reference.

Practical Example: On a UTM map of Colorado (central meridian 105°W) at a location 2° east of the central meridian with a magnetic variation of 10° east:

• Grid Convergence = +2° (east of central meridian)
• Magnetic Variation = +10°
• GMA = 2° – 10° = -8°
• To convert a grid bearing of 45° to magnetic: 45° – 8° = 37° magnetic

Can I use this calculator for historical magnetic variation research?

Yes, our calculator can provide historical magnetic variation data with some important considerations:

Capabilities:

• Accurate results from 1900 to present using the WMM and historical models
• Accounts for the significant changes in the Earth’s magnetic field over the past century
• Useful for historical navigation research, archaeological site analysis, and studying geomagnetic field evolution

Limitations:

• Pre-1900 Data: The calculator becomes less accurate for dates before 1900 as the WMM isn’t optimized for earlier periods. For pre-1900 research, consult the NOAA Historic Magnetic Field Calculator.
• Rapid Changes: Periods of geomagnetic jerks or pole movements may not be fully captured by the model’s linear interpolation.
• Local Anomalies: Historical mining activities or geological changes may have altered local magnetic fields in ways not reflected in the global model.

Historical Research Applications:

1. Ship Log Analysis: Reconstruct historical vessel routes by applying period-correct magnetic variations to compass bearings recorded in ship logs.
2. Archaeological Site Orientation: Determine the original orientation of ancient structures that were aligned using magnetic compasses.
3. Geophysical Studies: Track the movement of the magnetic poles and the evolution of the geomagnetic field over time.
4. Historical Map Verification: Verify the accuracy of declination information on vintage maps and charts.

Example: Analyzing the 1912 RMS Titanic’s distress coordinates shows that the magnetic variation at the wreck site (41.73°N, 49.95°W) was approximately 22° west in 1912, compared to about 18° west today. This 4° difference would have been critical for rescue operations and explains some of the navigational challenges faced by responding vessels.

How does altitude affect magnetic variation calculations?

Altitude has a measurable but generally small effect on magnetic variation for most practical applications. The relationship between altitude and magnetic field parameters follows these principles:

Physical Effects:

• Field Strength: The total magnetic field strength decreases with altitude approximately as 1/r³, where r is the distance from Earth’s center.
• Inclination: The angle between the magnetic field and the horizontal increases with altitude (the field becomes more vertical).
• Declination: The horizontal angle (variation) changes more slowly with altitude than other components, typically <0.1° per 1,000 meters.

Quantitative Effects:

Altitude (m)	Typical Variation Change	Field Strength Reduction	Practical Impact
0 (Sea Level)	Baseline	100%	Standard calculations apply
1,000	<0.1°	~97%	Negligible for most applications
5,000	<0.5°	~88%	Noticeable in precision surveying
10,000 (Cruising Altitude)	<1.0°	~75%	Significant for aviation navigation
30,000 (Stratosphere)	<3.0°	~30%	Specialized models required
100,000 (Near Space)	Unpredictable	~3%	Magnetic field dominated by external sources

When Altitude Matters:

• Aviation: At cruising altitudes (30,000-40,000 ft), the ~1° difference becomes significant over long distances. Modern flight management systems automatically account for this.
• Space Operations: Above 100km, the International Geomagnetic Reference Field (IGRF) becomes more appropriate than the WMM.
• High-Altitude Surveying: For geodetic surveys using aircraft or drones above 5,000m, altitude corrections should be applied.
• Balloon Experiments: Scientific balloons reaching the stratosphere require specialized magnetic field models.

Our Calculator’s Approach:

This tool includes altitude in its calculations using the International Association of Geomagnetism and Aeronomy (IAGA) approved altitude correction factors. The algorithm:

1. Applies the standard WMM at sea level
2. Adjusts the spherical harmonic coefficients for altitude using the potential theory
3. Recalculates the declination from the altitude-adjusted field components
4. Accounts for the reduced influence of crustal magnetic anomalies at higher altitudes

For most terrestrial applications (hiking, surveying, marine navigation), you can safely ignore the altitude parameter as the effect is minimal. The default value of 0 meters is appropriate for sea-level and low-altitude use cases.

What are the most common mistakes people make with magnetic variation?

Even experienced navigators sometimes make critical errors when working with magnetic variation. Here are the most common mistakes and how to avoid them:

Top 10 Magnetic Variation Mistakes

1. Using Outdated Data:
   • Problem: Relying on variation values from old maps or charts without checking current values.
   • Solution: Always verify with current models (like this calculator) before critical navigation.
   • Example: A 1980 map of Alaska might show 25° east variation, but current values are closer to 18° east – a 7° difference that could be disastrous.
2. Mixing East and West:
   • Problem: Adding when you should subtract (or vice versa) when converting between true and magnetic bearings.
   • Solution: Use the mnemonic “East is least, West is best” (add east variation, subtract west variation to get true from magnetic).
3. Ignoring Grid Convergence:
   • Problem: Assuming map grid lines point to true north when they actually converge with true north.
   • Solution: Always check the convergence angle shown in the map margin and apply it when working with grid bearings.
4. Compass Misadjustment:
   • Problem: Setting the declination adjustment incorrectly on an adjustable compass.
   • Solution: Double-check the adjustment using a known bearing before relying on it in the field.
5. Local Anomalies:
   • Problem: Not accounting for magnetic disturbances from iron deposits, power lines, or vehicles.
   • Solution: Take multiple compass readings in different locations and watch for inconsistencies.
6. Date Errors:
   • Problem: Using a variation value from the wrong year (especially problematic for historical research).
   • Solution: Always specify the correct date in calculations and check the annual change rate.
7. Unit Confusion:
   • Problem: Mixing degrees and mils (especially in military applications) or misinterpreting degrees/minutes.
   • Solution: Standardize on decimal degrees for calculations and verify unit consistency.
8. Polar Navigation Errors:
   • Problem: Assuming standard magnetic compasses work reliably near the magnetic poles.
   • Solution: Use gyrocompasses or GPS-based navigation in polar regions where magnetic fields are vertical.
9. Overlooking Annual Change:
   • Problem: Not accounting for the yearly change in variation when planning future expeditions.
   • Solution: Calculate the expected variation for your future trip date, not the current date.
10. Digital Overreliance:
    • Problem: Assuming GPS or digital compasses don’t need variation corrections.
    • Solution: Remember that GPS provides true north, while magnetic compasses (even digital ones) are affected by variation.

Verification Checklist:

Before relying on any magnetic variation calculation:

1. Cross-check with at least one other source (e.g., NOAA calculator, current aeronautical chart)
2. Verify the date of the magnetic information matches your needs
3. Confirm the location coordinates are accurate (decimal degrees vs. DMS)
4. Check for local anomalies if you’re in a mining area or near large metal structures
5. Test your compass adjustment with a known bearing before critical use
6. For aviation/marine use, confirm the variation matches your current flight plan or nautical chart

Are there any locations where magnetic compasses are unreliable?

Yes, there are several regions and situations where magnetic compasses become unreliable or completely unusable:

Geographic Problem Areas:

Magnetic Poles

• North Magnetic Pole: Currently near 86.50°N, 164.00°E (moving rapidly)
• South Magnetic Pole: Near 64.00°S, 135.00°E
• Issue: Compass needles point downward (dip) and spin freely, making horizontal navigation impossible
• Range: Unreliable within ~1,000km of either pole

Agonic Line

• Definition: Line where magnetic variation is 0° (magnetic north = true north)
• Current Location: Runs through Lake Superior, Florida, Gulf of Mexico, and southern South America
• Issue: Rapid changes in variation near this line can cause navigation errors
• Range: Problematic within ~200km of the line

Magnetic Anomalies

• Kursk Anomaly (Russia): Largest known, covers 150,000 km² with variations up to 10° from expected values
• Temagami Anomaly (Canada): Causes compass needles to spin 180° in some areas
• Iron Mountain (USA): Michigan’s Upper Peninsula has deposits causing 30°+ local deviations
• Pilbara Region (Australia): Iron ore deposits create navigation hazards for miners

High-Latitude Regions

• Arctic/Ocean: Above 70°N, compass needles dip significantly and become sluggish
• Antarctic: Similar issues below 70°S, compounded by ice movement
• Issue: Magnetic field lines become nearly vertical, reducing horizontal component
• Solution: Use gyrocompasses or GPS for primary navigation

Environmental Factors:

• Electrical Storms: Lightning and solar storms can cause temporary compass deviations of several degrees
• Power Lines: High-voltage lines create magnetic fields that can deflect compass needles by 10°+ within 100m
• Vehicles/Equipment: Metal vehicles, weapons, or tools can create local magnetic fields
• Mineral Deposits: Even small iron or nickel deposits can create localized anomalies
• Volcanic Activity: Magma movement can temporarily alter local magnetic fields

Alternatives for Problem Areas:

Problem Area	Alternative Navigation Method	Accuracy	Limitations
Magnetic Poles	Gyrocompass	±0.1°	Requires power, sensitive to movement
Magnetic Anomalies	GPS with true north reference	±3m	Requires clear sky view, battery dependent
High Latitudes	Star/Sun Navigation	±0.5°	Requires clear weather and training
Urban Areas	Digital compass with calibration	±1°	Can be affected by electronics
All Areas	Inertial Navigation System	±0.01°	Expensive, requires initial alignment

Special Considerations:

• Marine Navigation: Ships use gyrocompasses as primary navigation instruments, with magnetic compasses as backup. The gyrocompass finds true north by sensing Earth’s rotation.
• Aviation: Aircraft use fluxgate compasses that are less susceptible to acceleration errors than magnetic compasses, combined with GPS for modern navigation.
• Surveying: Professional surveyors use total stations that measure angles relative to vertical, avoiding magnetic issues entirely.
• Military: Advanced navigation systems integrate GPS, inertial navigation, and terrain matching to overcome magnetic limitations.