Swiss Micros DM32: Estimating Earth’s Acceleration at Latitude
Introduction
Earth’s gravitational force is usually set a constant of 9.80665 m/s², usually shortened to 9.8 m/s² or 9.81 m/s² in publications such as physics text books. However, in reality gravity on Earth is not constant. There are many ways to calculate (estimate) the gravitational acceleration depending where you are on Earth. Gravity depends on many factors including latitude (degrees North or South) and the elevation. The blog focuses on the effect of latitude on Earth’s gravity.
The is part of the Acceleration Due to Gravity table from the Desk Ref book (see the Source section). The column for m/s² is added.
Degrees Latitude (North or South) |
Gravity Acceleration (cm/s²) |
Gravity Acceleration (m/s²) |
0 (Equator) |
978.0327 |
9.780327 |
15 |
978.3786 |
9.783786 |
30 |
979.3249 |
9.793249 |
45 |
980.6199 |
9.806199 |
60 |
981.9178 |
9.819178 |
75 |
982.8698 |
9.828698 |
90 |
983.2186 |
9.832186 |
[Glover, Young, pg. 587]
There are many ways to estimate the gravitational acceleration depending where you are on Earth. Gravity depends on many factors including latitude (degrees North or South) and the elevation.
Earth’s gravity tends to be at the strongest at the poles. However, gravity weakens at higher elevations, where we are further away from the center of the planet.
Gravity Estimate – (Univ. of Illinois)
The formula that is presented by The Grainger College of Engineering Physics Van [Univ. of Illinois] is a simple but pretty accurate estimation of gravity:
g = g_45 – 1 / 2 * (g_poles – g_equator) * cos(2 * latitude * π ÷ 180)
where:
g_poles = 9.832 m/s²
g_45 = 9.806 m/s²
g_equator = 9.78 m/s²
lat = latitude, north or south
2 * latitude is converted to radians. (as it is multiplied by π ÷ 180)
Simplifying the equation leads to:
1 / 2 * (g_poles – g_equator) = 1 / 2 * (9.832 – 9.78) = 0.026
2 * latitude * π ÷ 180 = latitude * π ÷ 90 (in radians)
Then:
g = 9.806 – 0.026 * cos(latitude * π ÷ 90)
(in radians)
DM32 Program: Gravity Estimate
Input L as D.MS (degrees/minutes/seconds) format.
E01
LBL E
E02 RAD
E03 INPUT L
E04 →HR
E05 90
E06
÷
E07 π
E08 ×
E09 COS
E10 0.026
E11 ×
E12
+/-
E13 9.806
E14 +
E15 STO G
E16 RTN
World Geodetic System 84 Ellipsoidal Gravity Formula
The formula is presented by the World Geodetic System (WGS): [Wikipedia]
g = Ge * ((1 + k * sin² L) ÷ √(1 – e² * sin² L))
L: latitude in decimal degrees
with the constants:
Ge = 9.7803253359 m/s²
k = 0.001931852652
e² = 0.0066943799901
Input L as D.MS (degrees/minutes/seconds) format.
DM32: WEG ‘84
G01
LBL G
G02 DEG
G03 INPUT L
G04 →HR
G05 SIN
G06
x²
G07 STO T
G08 0.001931852652
G09 ×
G10 1
G11
+
G12 1
G13 RCL T
G14 0.0066943799901
G15 ×
G16
-
G17 SQRT
G18 ÷
G19 9.7803253359
G20 ×
G21
STO G
G22 RTN
Table of Values
Sources
“Gravity of Earth” Wikipedia. (2026, January 31).
https://en.wikipedia.org/wiki/Gravity_of_Earth Retrieved March 9, 2026.
Grainger Engineering Office of Marketing and Communications. (answer written by Rebecca H.) (2016, November 21). “How gravitational force varies at different locations on Earth.” Illinois. https://van.physics.illinois.edu/ask/listing/64061. Retrieved March 10, 2026.
Glover, Thomas J. and Richard A. Young. Desk Ref. Sequoia Publishing, Inc. Anchorage, AK 4th Edition. 2022 pg. 587
Eddie
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