About the Gravitational Force Calculator
This gravitational force calculator applies Newton's law of universal gravitation to any two objects. Enter both masses and the distance between their centres and it returns the attractive force in newtons (and pounds-force), shown in scientific notation for astronomical numbers, plus the acceleration each body gives the other.
Mass can be entered in grams, kilograms, pounds, tonnes, Moon masses, Earth masses or solar masses, and distance in metres, kilometres, miles, Earth radii or astronomical units — so you can compare the pull of the Earth on you, the Earth–Moon attraction or the Sun holding a planet in orbit without typing long exponents.
Distance is always measured centre to centre. For spherical bodies such as planets that makes the law exact outside their surface; for people or everyday objects close together it is an approximation. The gravitational constant used is the CODATA 2018 value G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻².
With the default inputs, the gravitational force is 687.4212 N. Change any value above to recalculate instantly.
How to use the gravitational force calculator
- 1Enter the first mass and choose its unit.
- 2Enter the second mass and choose its unit.
- 3Enter the centre-to-centre distance and its unit.
- 4Read the force in newtons and scientific notation, and the acceleration each mass feels.
Formula and method
Newton's law of universal gravitation says every pair of masses attracts with a force proportional to the product of the masses and inversely proportional to the square of the distance between their centres. G is the universal gravitational constant.
The calculator converts masses to kilograms and distance to metres, applies the formula and reports the force in newtons (1 lbf = 4.44822 N). Dividing the force by each mass gives the acceleration that body experiences — at Earth’s surface, G·M/R² works out to about 9.82 m/s², close to standard gravity. Relativistic effects are ignored, which is fine except near black holes or for precise orbital work.
- F
- Gravitational force (N)
- G
- Gravitational constant, 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²
- m₁, m₂
- The two masses (kg)
- r
- Distance between centres of mass (m)
Worked examples
Earth pulling on a 70 kg person
F = 6.6743 × 10⁻¹¹ × 5.9722 × 10²⁴ × 70 ÷ (6.371 × 10⁶)² ≈ 687 N — the person’s weight. Dividing by 70 kg gives about 9.82 m/s².
Earth and Moon
With the Moon (7.342 × 10²² kg) at an average 384,400 km, F ≈ 1.98 × 10²⁰ N. That force keeps the Moon in orbit and drives the ocean tides.
Two people 1 m apart
F = 6.6743 × 10⁻¹¹ × 80 × 60 ÷ 1² ≈ 3.2 × 10⁻⁷ N — about the weight of a grain of fine dust, which is why we never notice it.
Frequently asked questions
What is Newton's law of universal gravitation?+
It states that any two masses attract each other with a force F = G·m₁·m₂/r², where r is the distance between their centres and G is the gravitational constant. Isaac Newton published it in 1687.
What is the value of the gravitational constant G?+
The CODATA 2018 recommended value is G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², with a relative uncertainty of about 22 parts per million — one of the least precisely known fundamental constants.
Why is gravitational force so weak between everyday objects?+
G is tiny, so noticeable forces need enormous masses. Two 70 kg people standing 1 m apart attract with about 3 × 10⁻⁷ N, while the Earth pulls each of them with roughly 690 N.
What distance should I use for planets?+
Always use the distance between centres. For an object on a planet’s surface, that is the planet’s radius; for satellites, add the orbit altitude to the radius.
How is gravitational force related to weight?+
Weight is the gravitational force a planet exerts on you. Setting m₁ to the Earth’s mass and r to the Earth’s radius in the formula gives your weight, equal to mass × about 9.8 m/s².