(48G) Earth's Acceleration Estimation by Latitude

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(48G) Earth's Acceleration Estimation by Latitude - Eddie W. Shore - 2026-05-01 09:54

The true earth gravity force depends on several factors, such as latitude and altitude.  This estimation takes the latitude (north/south) into account. 

The constant 9.80665 m/s^2 is an accepted average, the true force varies. 

g_Earth = g_45-(g_poles + g_equ)/2*cos(lat*π/90 radians)
Simplified:  g_Earth = 9.806 - 0.026*cos(lat*π/90)

g_45 ≈ 9.806 m/s^2
g_poles ≈ 9.832 m/s^2
g_equ ≈ 9.78 m/s^2
Take the cosine of (latitude * π / 90) radians

gLAT:
Code:
<< RAD HMS→ 90 / π * →NUM COS
.026 * 9.806 SWAP - '1_m/s^2' * >>


Input:
1:  latitude in D.MMSS (degrees, minutes, seconds)
No need to enter units

Output:
1:  Earth's gravity at latitude_m/s^2  with unit object attached

Example:

Input: 
1:  20.2214 (20°22'14")

Output:
1:  ≈ 9.7863_m/s^2


Source:
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.


RE: (48G) Earth's Acceleration Estimation by Latitude - Thomas Klemm - 2026-05-01 12:58

You could use DEG instead of RAD:
Code:
« DEG HMS→ 2. * COS .026 * 9.806 SWAP - '1_m/s^2' * »