Inputs
Results
- Distance r: 6371000 m
- Mass M: 5.972190 × 1024 kg
- G·M (μ): 3.986019 × 1014 m³/s²
- Force on 1 kg: 9.820286 N
Formula
g(r) = G · M / r²
Substitution
G = 6.674300 × 10-11 N·m²/kg² M = 5.972190 × 1024 kg r = 6.371000 × 106 m g = (G·M)/r² = 3.986019 × 1014 / (6.371000 × 106)² g = 9.820286 × 100 m/s²
How to use
- Pick a preset body or keep Custom, then set mass and surface radius.
- Choose distance mode: altitude above the surface (r = R + h) or direct distance from center.
- Enter values and units. The calculator converts to SI automatically.
- Press Calculate g to get field strength in m/s² and as a multiple of standard gravity.
- Review the derivation and substituted values to validate your setup.
FAQs
1) What equation does this calculator use?
It applies Newton’s law of universal gravitation for a spherically symmetric body: g(r) = G·M/r². Near the surface you can use r = R + h to include altitude.
2) Can I compute gravity at orbital altitude?
Yes. Select the altitude mode and enter the height above the surface. The tool sets r = R + h and returns the weaker field at that altitude.
3) Which units are supported?
Mass supports kg, g, and tonnes; lengths support meters and kilometers. Outputs are in SI: m/s² for field strength, and N for force on one kilogram.
4) Why is N/kg the same as m/s²?
Because 1 N = 1 kg·m/s². Dividing newtons by kilograms gives m/s², so gravitational field strength and gravitational acceleration share the same numeric value.
5) Why is my surface value not exactly 9.80665 m/s² on Earth?
This calculator assumes a spherical Earth. Real values vary with latitude, elevation, and local geology. Standard gravity g0 = 9.80665 m/s² is a conventional average.
6) What is μ = G·M shown in the results?
It is the gravitational parameter, widely used in orbital mechanics. Using μ simplifies many equations and often has tighter uncertainty than G and M separately.
7) Can I compare two bodies?
Run the calculator twice with different presets or masses. Compare g values or the ratio to standard gravity to understand how surface gravity differs between bodies.