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Physics

Gravitational Force Calculator

F = G m₁ m₂ / r². Free online Gravitational Force Calculator. Calculate gravitational force online — fast, accurate, mobile-friendly, no signup needed.

F (N)
687.367242

Derivation

  1. ├── 01Givenm1 = 5.972e+24, m2 = 70, r = 6371000
  2. ├── 02Formula6674e-14 × t × a / (n²)
  3. └── 03Compute F (N)687.367242
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§01What is

Understanding the Gravitational Force Calculator

The Gravitational Force Calculator computes F (N) from 3 inputs: m₁ (kg), m₂ (kg), distance (m). F = G m₁ m₂ / r².

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Gravitational Force Calculator sits in that toolkit — it F = G m₁ m₂ / r². Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

6674e-14 × t × a / (n²)

Where

m1
m₁ (kg)
m2
m₂ (kg)
r
Distance (m)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: m₁ (kg) = 5.972e+24, m₂ (kg) = 70, Distance (m) = 6371000.

  1. 01Start by noting the input — m₁ (kg): 5.972e+24.
  2. 02Start by noting the input — m₂ (kg): 70.
  3. 03Start by noting the input — Distance (m): 6371000.
  4. 04Substitute these values into the formula: 6674e-14 × t × a / (n²)
  5. 05Compute F (N): the calculator returns 687.367.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Gravitational Force Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

m₁ (kg) halved

m1 = 2.98600e+24 (from 5.97200e+24)

Keep every other input at its default and halve the m₁ (kg). See how f (n) responds.

  1. 01New m₁ (kg): 2.98600e+24
  2. 02Baseline F (N): 687.367
  3. 03New F (N): 343.684
  4. 04F (N) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

m₁ (kg) doubled

m1 = 1.19440e+25 (from 5.97200e+24)

Keep every other input at its default and double the m₁ (kg). See how f (n) responds.

  1. 01New m₁ (kg): 1.19440e+25
  2. 02Baseline F (N): 687.367
  3. 03New F (N): 1374.73
  4. 04F (N) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

m₂ (kg) halved

m2 = 35 (from 70)

Keep every other input at its default and halve the m₂ (kg). See how f (n) responds.

  1. 01New m₂ (kg): 35
  2. 02Baseline F (N): 687.367
  3. 03New F (N): 343.684
  4. 04F (N) decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

m₂ (kg) doubled

m2 = 140 (from 70)

Keep every other input at its default and double the m₂ (kg). See how f (n) responds.

  1. 01New m₂ (kg): 140
  2. 02Baseline F (N): 687.367
  3. 03New F (N): 1374.73
  4. 04F (N) increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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