Formula used
The calculator uses Newton’s law of gravitation. For a mass M at a distance r from its center, the gravitational acceleration is:
For altitude mode, the distance is computed as r = R + h, where R is the mean radius and h is altitude above the surface.
For the uniform‑sphere “inside” option, the approximation is g(r) = G·M·r / R³, which grows linearly from the center to the surface.
How to use this calculator
- Select a calculation mode (mass & distance, altitude, density estimate, or inside‑sphere).
- Pick a reference body to auto‑fill mass/radius, or choose Custom to enter your own.
- Enter the needed inputs, choose units, and adjust precision if required.
- Click Calculate to view g in m/s², ft/s², and as a multiple of standard gravity.
- Use the download buttons to export your latest result as CSV or PDF.
Example data table
| Scenario | Mode | Inputs (typical) | Output g (m/s²) |
|---|---|---|---|
| Earth surface | Altitude | M=Earth, R=Earth, h=0 km | ~9.82 |
| ISS altitude | Altitude | M=Earth, R=Earth, h=400 km | ~8.69 |
| Moon surface | Altitude | M=Moon, R=Moon, h=0 km | ~1.62 |
| Near Mars orbit | Mass & distance | M=Mars, r=4000 km from center | ~2.67 |
| Uniform sphere estimate | Density | ρ=5514 kg/m³, R=Earth, h=0 km | ~9.82 |
Examples are approximate and depend on chosen constants and rounding.
1) What gravitational acceleration means
Gravitational acceleration, g, is the pull a mass creates at a point in space. It tells how quickly velocity changes when gravity is the only force. On Earth’s surface, g is near 9.81 m/s², meaning a falling object gains about 9.81 m/s each second. Standard gravity g₀ is defined as 9.80665 m/s², a useful reference for engineering comparisons worldwide in practice in many fields.
2) Why distance matters more than altitude
Gravity weakens with the square of distance from the center: g ∝ 1/r². Earth’s mean radius is about 6,371 km. At 400 km altitude, r rises to 6,771 km, so g drops to roughly 8.69 m/s²—about 11% lower than surface standard gravity.
3) Comparing common bodies
Different masses and radii create very different g values. The Moon is about 1.62 m/s², so a 70 kg person “weighs” near 113 N there. Mars is about 3.71 m/s², while Jupiter is about 24.8 m/s², over 2.5× Earth’s standard gravity.
4) Using density to estimate unknown mass
If you know average density ρ and radius R, mass can be estimated by M = ρ·(4/3)πR³. Using ρ ≈ 5514 kg/m³ and Earth’s radius returns a mass close to 5.97×10²⁴ kg, producing a surface g near 9.8 m/s² in this simplified model.
5) Gravity inside a uniform sphere
Inside a uniform sphere, gravity scales linearly with distance from the center: g(r) = GM·r/R³. At half the radius (r = 0.5R), g is about half the surface value. This is an approximation; real planets have layered density, so profiles differ.
6) Turning g into weight
This calculator can convert acceleration into weight using W = m·g. A 1 kg test mass weighs 9.81 N at Earth‑like gravity, 1.62 N on the Moon, and about 24.8 N on Jupiter. In pound‑force, 1 N equals about 0.22481 lbf.
7) Practical accuracy tips
Choose units carefully and enter r as distance from the center, not the surface. For altitude, use r = R + h. Small changes in radius can shift g by noticeable percentages. For high precision, keep G consistent, and remember rotation and latitude can alter Earth g by about 0.5%.
FAQs
1) What value of g should I use for Earth?
For quick work, use standard gravity g₀ = 9.80665 m/s². For location‑specific results, compute g with Earth’s mass and radius, or use altitude mode. Real Earth gravity varies slightly with latitude and elevation.
2) Why is gravity still strong in low orbit?
Orbiting objects are still close to Earth’s center. At about 400 km altitude, g is roughly 8.7 m/s². Astronauts feel weightless because they are in continuous free‑fall, not because gravity disappears.
3) Should I enter altitude or distance r?
Use altitude mode when you know surface radius R and height h, because it sets r = R + h. Use mass & distance mode when you already know r from the center, such as a satellite’s orbital radius.
4) Does the inside‑sphere option model real planets?
It uses a uniform‑density approximation where g decreases linearly toward the center. Real planets have layered density and rotation, so the true internal profile differs. Use it for learning, rough checks, or idealized spheres.
5) Does this calculator include rotation or latitude effects?
No. It computes gravitational acceleration from Newtonian gravity and a simple uniform‑sphere option. Apparent gravity on Earth is slightly reduced by rotation and varies with latitude and terrain.
6) Can I calculate weight in newtons and pounds‑force?
Yes. Enter a test mass to compute W = m·g in newtons, then it also converts to pound‑force (lbf). This is useful for comparing the same object’s weight on Earth, the Moon, Mars, or custom bodies.