This Online Calculator for Normal Gravity uses Markku Heikkinen Formula (Markku Heikkinen. Solving the shape of the Earth by using digital density models. Report 81:2, Finnish Geodetic Institute, Helsinki, 1981.). The formula is available in the book Geodesy: The science underneath by Martin Vermeer, page 431, TABLEAU 16.1
The formula for normal gravity, m/s2:
∂U/∂h = -9.78032677 - 0.05163075*sin2φ - 0.00022761*sin4φ - 0.00000123*sin6φ +
+ (+0.03087798 - 0.00004390*sin2φ - 0.00000020*sin4φ)*10-4*h +
+ (-0.00007265 + 0.00000021*sin2φ)*10-8*h2 + 0.00000015*10-12*h3 + ...
Where
φ - geodetic latitude, degrees;
h - Altitude, m.
The Markku Heikkinen Formula considers the attraction by the Earth’s masses and centrifugal forces caused by the Earth’s rotation.
The Precision of the calculator can be adjusted.