Gravitational Force Calculator
Newton's law of gravitation F = Gm₁m₂/r², with an Earth preset for weight-at-altitude problems.
What is Gravitational Force?
Every pair of masses attracts with F = G m₁ m₂ ÷ r², where G = 6.674 × 10⁻¹¹ N·m²/kg² and r is the distance between their centres. The constant is so small that everyday masses attract with forces far below a newton — it takes a planet to make the law visible, which is why the Earth preset reproduces the familiar 9.8 N on a 1 kg mass and why weight is just this law at the planet's surface.
How it works
F = G m₁ m₂ ÷ r², solved for whichever of the four is left blank — including the separation, which is the inverse-square step most rearrangements fumble. Masses go in kilograms and separations in the unit you choose, converted before the arithmetic. The sample fills Earth's mass (5.972 × 10²⁴ kg) and radius (6 371 km) against a 1 kg mass; for an altitude question, r is the radius plus the altitude, because the separation is centre-to-centre.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
Why does the Earth preset give 9.8 N on a 1 kg mass?
Because g is this law in disguise: g = G M ÷ R² with Earth's mass and radius gives 9.8 m/s². Weight is F = mg, so 1 kg at the surface feels 9.8 N — the same number the force calculator produces from the acceleration directly.
What separation do I use for an altitude problem?
Earth's radius plus the altitude. The law acts between centres, so a satellite at 400 km sits at r ≈ 6 771 km, not 400 km — and that difference is why its weight is about 89% of the surface value rather than a rounding error.
Why don't I feel the gravitational pull of the person next to me?
Because G is tiny. Two 70 kg people a metre apart attract with about 3 × 10⁻⁷ N — the weight of a grain of dust, drowned out entirely by Earth's pull and by friction in your shoes. The law never stops acting; the constant just keeps it honest.