Gravitational Force Calculator

Gravitational force is the attractive force that every object with mass exerts on every other object with mass. It is one of the four fundamental forces of nature and the dominant force at astronomical scales. Isaac Newton formulated the law of universal gravitation in 1687, stating that the gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This inverse-square law means that doubling the separation between two objects reduces the gravitational force to one quarter of its original value. Our gravitational force calculator applies this law precisely using the CODATA 2018 value of the gravitational constant G = 6.674 × 10⁻¹¹ N·m²·kg⁻².

1. 1. Enter the Two Masses: Input the values of m₁ and m₂ in any supported unit — kg, g, lb, tonne, solar mass, or Earth mass. Scientific notation is fully supported (e.g. 5.972e24 for Earth's mass). All processing happens locally in your browser — your data never leaves your device.
2. 2. Enter the Distance and Choose Output Unit: Enter the centre-to-centre distance r in m, km, AU, light-years, or other units. Select your preferred output force unit (N, kN, lbf, dyn, or kgf). Click "Calculate Force" and the gravitational force calculator instantly applies F = G × m₁ × m₂ / r².
3. 3. Review Results and Steps: The result is displayed in your chosen unit alongside conversions to N, kN, lbf, and dyn. Toggle the step-by-step solution to see every stage of the calculation with intermediate values in scientific notation.

• Gravitational Force (F): Computed using F = G × m₁ × m₂ / r², where G is Newton's gravitational constant. The result is always an attractive force — it acts along the line joining the two masses, pulling them toward each other.
• Unit Conversions: The gravitational force calculator automatically converts the result to N, kN, lbf, and dyn so you can compare values across different unit systems without additional steps.
• SI Unit Normalisation: All input values are internally converted to SI units (kg and m) before the calculation, ensuring accuracy regardless of which input units you choose.
• Step-by-Step Working: The gravitational force calculator shows every intermediate value — unit conversions, r², the numerator G × m₁ × m₂, and the final division — so you can verify each stage of the calculation.

Newton's law of universal gravitation treats masses as point masses or uniform spheres. For uniform spheres, the distance r is measured between their centres. The law is an excellent approximation for most practical and astronomical calculations, but for extreme gravitational fields — such as near black holes or neutron stars — Einstein's general theory of relativity provides a more accurate description. Gravitational force is always attractive; there is no gravitational repulsion. The gravitational force calculator uses the CODATA 2018 recommended value G = 6.674 × 10⁻¹¹ N·m²·kg⁻², which has a relative standard uncertainty of 2.2 × 10⁻⁵.