Calculate Gravity: Formula, Examples, and Earth’s Value

Calculate gravitational acceleration from the mass of a body and your distance from its center using Newton’s formula. Enter mass in kilograms and distance in meters to get gravity in meters per second squared, with the equivalent in feet per second squared as a helper result.

Formula

For a spherical body, the gravitational acceleration at distance r from its center is g = GM / r². Here, g is gravitational acceleration in meters per second squared (m/s²), G is the universal gravitational constant, approximately 6.67430 × 10⁻¹¹ m³/(kg·s²), M is the attracting body’s mass in kilograms (kg), and r is the distance from the body’s center in meters (m). The calculator uses this standard value of G and converts the answer to feet per second squared (ft/s²) for comparison.

Gravity is an acceleration, not a force. To calculate the gravitational force on an object of mass m_o, use F = m_og, where force F is measured in newtons (N) if mass is in kilograms and g is in m/s². For example, an object with a mass of 2 kg near Earth’s surface experiences a gravitational force of about 19.6 N.

Worked Example

Using the calculator’s default values, Earth has mass M = 5.972 × 10²⁴ kg and the distance from its center is r = 6,371,000 m.

1. Square the distance: r² = 6,371,000² = 40,589,641,000,000 m².
2. Multiply the gravitational constant by Earth’s mass: GM = (6.67430 × 10⁻¹¹)(5.972 × 10²⁴) ≈ 3.98589 × 10¹⁴ m³/s².
3. Divide by the squared distance: g = GM/r² ≈ 9.82 m/s².
4. Convert to customary units: 9.82 × 3.28084 ≈ 32.22 ft/s².

The calculator therefore returns 9.82 m/s², or 32.22 ft/s², rounded to two decimal places. This is an idealized estimate for Earth at a distance equal to its mean radius.

What Gravity Measures

Gravity is the acceleration caused by gravitational attraction. Near Earth’s surface, objects in free fall accelerate at roughly 9.8 m/s², which means their downward speed increases by about 9.8 meters per second for each second of falling, if air resistance is ignored. In customary units, that is about 32.2 ft/s².

The value is not exactly the same everywhere. Earth’s rotation, its slightly flattened shape, elevation, and local variations in the distribution of mass all affect measured surface gravity. The familiar value of 9.80665 m/s² is a conventional standard gravity used for reference and calculations; it is not a precise measurement at every location.

How to Choose the Distance

The distance in the formula is measured from the center of the attracting body, not from its surface. At Earth’s surface, use Earth’s radius, about 6.371 million meters on average. At an altitude h above the surface, use r = R + h, where R is the body’s radius and both distances use the same units.

• At Earth’s surface: set r to the radius from Earth’s center to the surface.
• Above Earth: add altitude to Earth’s radius. For an altitude of 400 km, use approximately 6,771 km from the center.
• Near another spherical body: enter that body’s mass and the distance from its center, using matching SI units.

Because distance is squared in the denominator, increasing the distance reduces gravity quickly. At twice the distance from a body’s center, the gravitational acceleration is one quarter as strong, assuming the same body and a point outside it.

When This Calculation Applies

The equation is useful for estimating gravity around planets, moons, and other roughly spherical bodies when their mass and your distance from the center are known. It also explains why an object’s weight changes with location: its mass stays the same, but the local gravitational acceleration can differ.

The simple formula treats the body’s mass as if it were concentrated at its center. For a spherical body with a symmetric mass distribution, Newton’s shell theorem makes this calculation valid outside the body. It is not generally enough for locations inside a planet, for irregular bodies nearby, or for precision work that needs rotation and local geology included.

Common Mistakes and Limits

• Using altitude alone: altitude is not the center-to-center distance; add the body’s radius.
• Mixing units: this calculator expects kilograms and meters. Convert grams to kilograms and kilometers to meters before entering values.
• Confusing gravity with weight: g is acceleration. Weight is a force and also depends on the object’s mass.
• Assuming a universal Earth value: 9.8 m/s² is a useful approximation, not an exact local reading.
• Rounding too early: keep full precision through the calculation, then round the final result to the precision appropriate for the inputs.

For everyday estimates, Newton’s formula is usually sufficient. Very precise predictions of motion near massive objects may require a more complete model, including planetary rotation, nonspherical mass distribution, or, in extreme gravitational fields, general relativity.

Frequently Asked Questions

How do you calculate gravity?
Use g = GM/r²: multiply the body’s mass by the gravitational constant, then divide by the square of your distance from its center. Use kilograms and meters for the units shown here.

What is gravity on Earth?
Near Earth’s surface, gravitational acceleration is approximately 9.8 m/s², or 32.2 ft/s². The exact local value varies slightly with location and elevation.

Does gravity depend on an object’s mass?
The gravitational acceleration caused by a planet does not depend on the mass of a small falling object in the ideal model. The force on that object does: F = m_og.

How does gravity change with height?
It decreases according to the inverse-square law. Calculate the distance from the planet’s center by adding altitude to its radius, then use g = GM/r².

Is gravity the same as weight?
No. Gravity is commonly used to mean gravitational acceleration, measured in m/s². Weight is the gravitational force on an object, measured in newtons in SI units.

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in m | Mass of attracting body | kg | 5.972e24 | 0
in r | Distance from center | m | 6371000 | 0
out g | Gravitational acceleration | m/s² | 6.67430e-11 * m / (r ^ 2) | 2
out us | Gravitational acceleration | ft/s² | g * 3.28084 | 2