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Compass Errors &
Earth's Magnetic Field
Calculator

More functions than your average e6b:

Calculate and graph compass errors for anywhere on Earth using official2
World Magnetic Models: WMM 2015 to WMM 2025 (2015 to 2029 coverage)
Introduction

The Ultimate Aviation Compass and Magnetic Field Calculator

Welcome to the most comprehensive World Magnetic Model (WMM) calculator for pilots and aviation enthusiasts. This powerful tool provides precise calculations for magnetic declination (variation), inclination (dip), and magnetic field strength (in nT) using the WMM 2015, WMM 2020, and WMM 2025 models. Go beyond simple declination and explore the dynamic turning and acceleration errors that affect a magnetic compass in flight. Our interactive calculators and graphs allow you to visualize complex concepts like turning lead and lag, critical tilt angles, and compass overshoot, providing an unparalleled educational experience for mastering this critical navigation instrument.

Page Table of Contents

Use these links to go directly to desired section
Video Tutorials (Compass Errors)
Overview of Parts I, II and II Using Part II - Compass Errors Calculator
Using Part I - Magnetic Field From Lat Long
Compass Errors
Part I - Magnetic Field From Lat Long Part III - Graphs
Part II - Compass Errors Calculator

Magnetic Field Model
Declination (Variation)
Magnetic Dip (Inclination)
& Compass Errors




*Requires location services to be enabled / allowed.
Note: The appropriate WMM model (2015,2020 or 2025) will be chosen based on date eneterd below

Part I - Magnetic Field from Latitude and Longitude and Compass Errors

Main Variables (Input)

Latitude o ' " or o or o S N
Longitude o ' " or o or o W E
1Altitude [m] [ft] [km] [sm]
Date (2015--2029) [year] [month] [day]

2Calculated Results (Output)
Declination / Variation [ o ] -W +E Change [ o/yr ] -W + E Uncertainty [ o ]
Inclination / Magnetic Dip [ o ] +Dn / -Up Change [ o/yr ] +Dn / -Up Uncertainty [ o ]
Horizontal Field Intensity [nT] Change [nT/yr ] Uncertainty [nT]
Vertical Field Intensity [nT] Change [nT/yr ] Uncertainty [nT]
North Field Component [nT] Change [nT/yr ] Uncertainty [nT]
East Field Component [nT] Change [nT/yr ] Uncertainty [nT]
Total Field [nT] Change [nT/yr ] Uncertainty [nT]

3D Declination (Variation) and Inclination (Dip) Visualization - Brown vector represents magnetic field (Output)

Browser doesn't support Canvas graphics

Compass Effects / Errors (Output)

Horizontal Field Suitability
XXXXXXXX
Compass indicated magnetic heading at a magnetic heading of 360 for a given bank angle
Bank Angle 5o 10o 15o 20o 25o 30o 35o
Turning Left
Turning Right
Compass indicated magnetic heading at a magnetic heading of 180 for a given bank angle
Bank Angle 5o 10o 15o 20o 25o 30o 35o
Turning Left
Turning Right
Aircraft TAS [knots] [Km/h] [sm/h] [m/s]
Bank Angle Std Rate 1/2 Std Rate Bank Angle: [ o ] Custom: ± [ o ] ( 0o to 89.9o)
Compass indicated magnetic heading at a given magnetic heading at a bank angle for xxxxx
Magnetic Heading 360 010 020 030 040 050 060
Turning Left
Turning Right
Magnetic Heading 070 080 090 100 110 120 130
Turning Left
Turning Right
Magnetic Heading 140 150 160 170 180 190 200
Turning Left
Turning Right
Magnetic Heading 210 220 230 240 250 260 270
Turning Left
Turning Right
Magnetic Heading 280 290 300 310 320 330 340
Turning Left
Turning Right
Magnetic Heading 350 355 360 005 175 180 185
Turning Left
Turning Right
Compensating:
XXXXXXXXXX
Compass indicated magnetic heading when accelerating / decelerating on a 090magnetic heading for a given acceleration
g's 0.01 0.05 0.1 0.15 0.2 0.25 0.3
Accelerating
Decelerating
Compass indicated magnetic heading when accelerating / decelerating on a 270 magnetic heading for a given acceleration
g's 0.01 0.05 0.1 0.15 0.2 0.25 0.3
Accelerating
Decelerating
Compass indicated magnetic heading when accelerating / decelerating on a 045 magnetic heading for a given acceleration
g's 0.01 0.05 0.1 0.15 0.2 0.25 0.3
Accelerating
Decelerating
Compass indicated magnetic heading when accelerating / decelerating on a 135 magnetic heading for a given acceleration
g's 0.01 0.05 0.1 0.15 0.2 0.25 0.3
Accelerating
Decelerating
Compass indicated magnetic heading when accelerating / decelerating on a 315 magnetic heading for a given acceleration
g's 0.01 0.05 0.1 0.15 0.2 0.25 0.3
Accelerating
Decelerating
Compass indicated magnetic heading when accelerating / decelerating on a 225 magnetic heading for a given acceleration
g's 0.01 0.05 0.1 0.15 0.2 0.25 0.3
Accelerating
Decelerating
Note: assuming straight and level (constant altitude, no banking and maintaining a constant heading)
Compensating:
XXXXXXXXX

Part II - Compass Errors and Required Undershoot / Overshoot Calculator

Compass Indicated Magnetic Heading - Combined Bank & Acceleration

Calculator Options
Declination / Variation From calc mag field abv: [ o ] -W +E Cust val (-90o to 90o) [ o ] -W +E
Magnetic Dip From calc mag field abv: [ o ] +Dn / -Up Cust val (-89o to 89o) [ o ] +Dn / -Up
Main Variables
Magnetic Heading [ o ] or True Heading [ o ] Current Desired at rollout
Bank Angle [ o ] -Left +Right (range 0o to 89.9o)
Acceleration [g's] -decel +accel [m/s2] [ft/s2]
Indicated Magnetic Heading [ o ] Current To begin / lead rollout
Correlated Variables
For max compass turn rate calculation, assume: std rate TAS: [knots] TAS: [knots]
Compass Plane Tilt Angle Due to Bank (long. axis)*:
XXXXXXX
 Compass Plane Tilt Angle Due to Acceleration (lat. axis)*:
XXXXXXX
Compass Plane Total Resultant (not sum) Tilt Angle*:
XXXXXXX
 Critical Compass Plane Tilt Angle*:
XXXXXXX
Compass Plane Tilt Will Exceed Critical Tilt:
XXXXXXX
 Lowest |%| of Mag. Field Acting on Comp. Plane**:
XXXXXXX
Degrees Turned During Rollout:
XXXXXXX
 Max Compass Plane Turn Rate (through 360o)***:
XXXXXXX
Magnetic Heading at Rollout Start:
XXXXXXX
 Magnetic Heading after Rollout (Desired at rollout):
XXXXXXX
Compass Error at Rollout Start:
XXXXXXX
 Compass Error after Rollout (zero if no acceleration):
XXXXXXX
Indicated Magnetic Heading after Rollout (wings level):
XXXXXXX
 Compass Error -Undershoot / +Overshoot Component:
XXXXXXX
Bank Rollout Component (always -undershoot):
XXXXXXX
 Total Required -Undershoot / +Overshoot:
XXXXXXX
*In relation to horizon **If too weak compass may not turn to keep up with turn ***If too fast compass may not keep up due to inertia and friction
Note: all results assume zero inertia, zero friction and enough magnetic field component to act on compass plane

Part III - Graphs

Compass Errors Plot (Output)

Graph Options
General & Global
X axis: Aircraft Magnetic HDG Compass Indicated Magnetic HDG
Y axis: Relative Error Absolute
Grid - show: minor major Avoid critical compass tilt: [ o ]
Show graph local maxima / minima Animation: Speed Scale Fixed at max Auto
Inclination / Magnetic Dip
Multiple values No. values
Use from calculated magnetic field: [ o ] Use custom value (-90o to 90o) [ o ] +Dn / -Up
Animate
Inclination / Dip from [ o ] to [ o ] (range -90o to 90o) Step
Bank Angles
Multiple angles No. angles
User defined
Aircraft TAS [knots] [Km/h] [sm/h] [m/s]
Bank Angle Std Rate 1/2 Std Rate Bank Angle: ± [ o ]
Custom: ± [ o ] (range 0o to 89.9o)
Animate
Bank Angle from ± [ o ] to [ o ] (range 0o to 89.9o) Step
Acceleration
Multiple values No. values
User defined [g's] -decel +accel
Animate
Acceleration from [ o ] to [g] (range -100g to 100g) Step
Browser doesn't support Canvas graphics
Undershoot / Overshoot Graph | Relative Absolute
Component for compass error at the heading for start of rollout
Component for degrees turned during rollout (always undershoot and equal to ½ the bank angle)
Total required undershoot/overshoot to roll out at desired heading
Other Graphs
Compass disc required rotational speed to keep up with field position change
(1st derivative -- if too high, compass may not keep up due to friction) per deg or deg2
per s or s2 assume speed for std rate turn
per s or s2 for TAS [knots]
Compass disc required rotational acceleration to keep up with field position change
(2nd derivative -- if too high, compass may not keep up due to inertia)
Compass tilt angle (angle of compass disc plane in relation to the horizon) highlight> critical tilt (reversal region)
Vertical angle between compass disc plane and magnetic field vector highlight >90o (reversal region)
Component as a percentage of the total magnetic field that is parallel to the compass disc plane highlight reversal
1GPS altitude: In reference to World Geodetic System (WGS-84) height / altitude. The magnetic field differences in reference to sea level height are negligeable.

2References for the magnetic field calculation portion (field direction and strength based on Lat, Lon, altitude and date)
 Chulliat, A., W. Brown, P. Alken, C. Beggan, M. Nair, G. Cox, A. Woods, S. Macmillan, B. Meyer and M. Paniccia, 2020. The US/UK World Magnetic Model for 2020-2025: Technical Report, National Centers for Environmental Information,NOAA. doi: 10.25923/ytk1-yx35.
Besides WMM 2020 (valid for 1/1/2019 to 12/31/2024), also incorporates coeficients for WMM 2025 (valid for 1/1/2025 to 12/31/2029). Models selected according to date eneterd. Does not use the original authors of WMM model programs. Everything on this page has been programmed by Luiz Oliveira from scratch based on the white paper.

3Note: No portion of these calculators and graphs have been endorsed or verified by NOAA or any of the WMM white paper authors. Use is for educational and academic purposes only. LuizMonteiro assumes no responsibility for any inaccuracies or errors.


Navigation Simulator
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Free Online Simulators
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Units and Abbreviations
Magnetic Field Intensity
nT - nano Tesla
Length or Distance
m - meters
ft - feet
Nm - nautical miles
km - kilometers
sm - statute miles
Speed
knots - knots (Nm/h)
km/h - kilometers per hour
sm/h - statute miles per hour
m/s - meters per second
Time
yr - year
h or hr(s) - hour(s)
m or min(s) - minute(s)
s or sec(s) - second(s)
Angle
o - degrees or deg
' - minutes (1/60 deg)
'' - seconds (1/3600 deg)
Angular Speed & Acceleration
o/s - deg per second
o/s2 - deg per second squared

By Luiz Roberto Monteiro de Oliveira. Screenshots and video captures allowed (personal, business or military) as long as credited to author and link to this site or URL included. Permission required for all other uses.

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