This Online Calculator for Local Gravity uses WSG 84 ellipsoidal Gravity Formula from DMA TECHNICAL REPORT TR8350.2-a, Chapter 4. The formula is combined with the altitude correction formula from the book "Atmosphere-Ocean Dynamics" by A. E. Gill, 1982.

This is the formula of Somigliana that has been selected as the official WSG 84 ellipsoidal Gravity Formula:

γ = γ_{e}(1 + k*sin^{2}θ)/(1 - e^{2}*sin^{2}θ)^{1/2} (4-3)

Where

k = ((b * γ_{p})/(a * γ_{e})) - 1 = 0.00193185138639;

a, b - semi-major and semi-minor axes of the ellipsoid, respectively;

γ_{e} - theoretical gravity at the equator, γ_{e} = 9.7803267714 m/s^{2};

γ_{p} - theoretical gravity at the pole;

e^{2} - square of the first eccentricity of the ellipsoid, e^{2} = 0.00669437999013;

θ - geodetic latitude, degrees.

The formula (4-3) is used to calculate normal gravity on the ellipsoidal surface.

The same WGS 84 Ellipsoidal Gravity Formula, expressed numerically, is:

γ = 9.7803267714*(1 + 0.00193185138639*sin^{2}θ)/(1 - 0.00669437999013*sin^{2}θ)^{1/2} (4-4)

The formula from the book "Atmosphere-Ocean Dynamics" by A. E. Gill, 1982, Appendix Two, Useful Values, page 597:

g = (9.78032 + 0.005172*sin^{2}θ - 0.00006*sin^{2}(2θ))*(1 + z/a)^{-2} (Gill)

where

g - acceleration of the gravity, m/s^{2} as a function of latitude θ and altitude z;

z - altitude, m;

a - radius of sphere having the same volume as the earth, a = 6371000 m.

Combining the formula (4-4) and the right part of the Gill's formula ((1 + z/a)^{-2}), we get the very precise formula for the theoretical local gravity:

γ = γ_{e}*(1 + k*sin^{2}θ)/(1 - e^{2}*sin^{2}θ)^{1/2} * (1 + z/a)^{-2} (1)

And the same formula, expressed numerically:

γ = 9.7803267714*(1 + 0.00193185138639*sin^{2}θ)/(1 - 0.00669437999013*sin^{2}θ)^{1/2} * (1 + z/a)^{-2} (2)

This Local Gravity Calculator uses the formula shown above. All parameters (γ_{e}, a, k, e^{2}) may be changed if needed. The Precision of the calculator also can be adjusted.

All units used in formulas above and in this online calculator are MKS (Meter-Kilogram-Second) unit system.