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DIY Cost Tools

DIY Cost Tools

Gravitational Force Calculator

Estimate the magnitude of the Newtonian gravitational attraction between two point masses. Enter both masses in kilograms and the distance between their centers in metres.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the stated units and domain limits.

Force magnitude (N)8.342875e-10

How to use this calculator

  1. Enter every quantity in the unit printed beside its field.
  2. Select Calculate or press Enter.
  3. Read the labeled results and compare them with the assumptions below.

Formula and method

F = Gm₁m₂/r², using G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻².

The calculation runs locally in your browser. If any entry is invalid or a mathematical condition is undefined, the prior result is hidden so it cannot be mistaken for a new answer.

Worked example

Using Mass 1 (kg) = 5, Mass 2 (kg) = 10, Center-to-center distance (m) = 2, the formula returns Force magnitude (N) = 8.342875e-10. The displayed default result is generated from these same inputs.

Limitations and safety

Treats each object as a point mass, or as a spherically symmetric body observed outside it. It does not model relativistic effects, overlapping bodies, other forces or uncertainty in mass and position. Results use floating-point arithmetic and are displayed to about 10 significant digits; measurement uncertainty usually supports fewer. Verify units before relying on a result.

Frequently asked questions

Why is the default force so small?

Gravity between ordinary laboratory-sized masses is extremely weak. Large astronomical masses produce much larger forces.

Why might a measured result differ?

The formula isolates the stated model. Real systems can add uncertainty, losses, changing properties, geometry or forces that are not among the inputs.

How should I handle units?

Convert every value to the unit shown beside its field before calculating. A numerically valid value in the wrong unit will still produce a wrong result.

Review notes and reference

Reviewed October 3, 2026. The default example and an independent edge or scaling case were checked against expected values. The live script was also checked for blank, text, comma-formatted, non-finite and out-of-range entries. Method reference. Constants use the values stated in the formula. This page’s explanation and example are original.

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