Newton's Gravitational Force Calculator
Newton's gravitational force calculator (F = Gm₁m₂/r²): solve for force, mass or distance in SI units, with a US/imperial readout. Curriculum-aligned.
Newton's Gravitational Force Calculator
Enter any three values and leave the fourth blank — the calculator solves for it. Results are in SI units, with a US/imperial readout below.
- Curriculum
- English (global) — Cambridge International + IB
- Built against
- Cambridge International AS/A-Level Physics 9702 + IB Diploma (2023–2025) — Gravitational Fields
- Unit system
- SI primary; US/imperial readout below
- First published
- 1 Jun 2026
- Last updated
- 1 Jun 2026
View authoritative scientific sources
- NIST SP 811 (2008), §3 — units & conversions
- BIPM SI Brochure, 9th edition (2019)
- CODATA 2018 — gravitational constant G = 6.674×10⁻¹¹
- Newton's Law of Universal Gravitation — Encyclopædia Britannica
⚠️ Educational use only — see full disclaimer
EDUCATIONAL USE DISCLAIMER
This calculator is provided for educational and reference purposes only. It is not a substitute for instruction from a qualified teacher, your prescribed textbook, or your school's official curriculum materials.
When preparing for examinations, always cross-check our calculations and notation against your current syllabus and your teacher's guidance. Syllabus conventions and accepted notation vary between curricula and may change between examination years.
If you believe any calculation, notation, or curriculum reference in this tool is inaccurate, please let us know via the feedback button. We review feedback promptly and update tools when verified corrections are needed.
RECATOOLS accepts no liability for academic, examination, professional, or research outcomes arising from use of this tool.
How to Use the Gravitational Force Calculator
Pick your curriculum
Use the curriculum pills above to match your syllabus (Cambridge, SEAB, STPM, SBMPTN, 高考, 學測 or HKDSE). Terminology, the worked example and the whole page follow your selection.
Enter any three values
Type three of force, the two masses and the distance — leave the one you want to find blank. Each field has a unit selector (kg, g, t, lb; m, km, mile; N, kN, lb-f).
Read the SI result
The answer is shown in SI units — newtons (N), kilograms (kg), metres (m), with a dimmed US/imperial readout below that you can hide.
Check against your syllabus
The Tool Information block shows exactly which syllabus this is built against. Spot something off? Use the feedback button — we review every report.
Newton's Law of Gravitation, in Your Curriculum's Words
Newton's Law of Universal Gravitation
Example: The Earth (m₁ = 5.97 × 10²⁴ kg) and the Moon (m₂ = 7.35 × 10²² kg) are about r = 3.84 × 10⁸ m apart. The gravitational force between them is:
Given: G = 6.674 × 10⁻¹¹ N m² kg⁻². Using F = G m₁ m₂ / r²:
F ≈ 1.98 × 10²⁰ N
Newton's law of universal gravitation states that every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G m₁ m₂ / r². Force is in newtons (N), mass in kilograms (kg), distance in metres (m), and G is the gravitational constant, 6.674 × 10⁻¹¹ N m² kg⁻². Rearranged, the same law gives either mass or the distance, which is why this tool solves for whichever value you leave blank.
Gravity is the weakest of the four fundamental forces, so the force between everyday objects is minute — which is why results are often shown in scientific notation. SI is always the primary result, with a dimmed US/imperial readout for students whose textbooks use imperial units. All calculation happens in your browser — nothing is uploaded.
The gravitational pull between two apples on a table is real, but far too small to feel. The same law holds the Moon in its orbit.
10 Facts About Newton's Law of Gravitation
Newton published universal gravitation in his 1687 Principia.
The constant G ≈ 6.674 × 10⁻¹¹ N m² kg⁻² — among the least precisely known constants.
Gravity follows an inverse-square law: F ∝ 1/r².
Double the separation and the force drops to a quarter.
Gravitation is always attractive — there is no "anti-gravity" mass.
It acts between any two masses, however small.
Cavendish first measured G in 1798 with a torsion balance.
Your weight is just this force with Earth: F = GMm/r² = mg.
The same law drops an apple and keeps a planet in orbit.
This calculator runs in your browser — your working stays private.
Frequently Asked Questions
- F = G m₁ m₂ / r² — the gravitational force equals the gravitational constant G times the product of the two masses, divided by the square of the distance between them. Rearranged, the same law gives either mass (m₁ = F r² / (G m₂)) or the distance (r = √(G m₁ m₂ / F)). This calculator solves for whichever of the four you leave blank.
- SI units: newtons (N) for force, kilograms (kg) for mass, metres (m) for distance; G is in N m² kg⁻². You may enter other units (g, t, lb; km, mile; kN, lb-f); the tool converts to SI internally and shows the result in SI with a dimmed US/imperial readout below.
- Yes. Enter three of the four quantities (force, the two masses, the distance) and leave one blank — the calculator rearranges F = G m₁ m₂ / r² and solves for the missing value, including taking a square root when solving for distance.
- The calculator uses the CODATA 2018 value, G = 6.674 × 10⁻¹¹ N m² kg⁻². Note that some exam data booklets round this to 6.67 × 10⁻¹¹, so your answer may differ slightly in the last digit — check the value your syllabus prescribes.
- The physics — F = G m₁ m₂ / r² in SI units — is identical worldwide. What changes is the terminology, worked-example style and exam conventions. The selector matches those to your syllabus so the tool reads like your textbook.
- Gravity is the weakest of the four fundamental forces of nature. Between everyday objects it is all but undetectable; it only becomes significant when at least one mass is very large, like a planet or a star. That is why the calculator often shows results in scientific notation.
- Weight is the gravitational force between an object and the Earth. Setting g = GM/r² (where M is the Earth's mass), F = G M m / r² becomes F = mg. So mg is just the special case of universal gravitation near the Earth's surface.
- The Tool Information block lists the exact syllabus for your selected curriculum (e.g. Cambridge A-Level 9702 or SEAB H2 Physics 9749). It is a study aid, not a substitute for your official syllabus or teacher.
- No. Every calculation runs in your browser; nothing you type is uploaded. It works offline once the page has loaded.
- Completely free, no account or usage limit. It runs entirely in your browser and collects no data.
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