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Physics

Surface Gravity Calculator

g = GM/r². Free online Surface Gravity Calculator. Calculate surface gravity online — fast, accurate, mobile-friendly, no signup needed.

g (m/s²)
9.819532

Derivation

  1. ├── 01GivenM = 5.972e+24, r = 6371000
  2. ├── 02Formula6674e-14 × t / (a²)
  3. └── 03Compute g (m/s²)9.819532
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§01What is

Understanding the Surface Gravity Calculator

The Surface Gravity Calculator computes g (m/s²) from 2 inputs: mass (kg), radius (m). g = GM/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 Surface Gravity Calculator sits in that toolkit — it g = GM/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 / (a²)

Where

M
Mass (kg)
r
Radius (m)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Mass (kg) = 5.972e+24, Radius (m) = 6371000.

  1. 01Start by noting the input — Mass (kg): 5.972e+24.
  2. 02Start by noting the input — Radius (m): 6371000.
  3. 03Substitute these values into the formula: 6674e-14 × t / (a²)
  4. 04Compute g (m/s²): the calculator returns 9.81953.
  5. 05Cross-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 Surface Gravity 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

Mass (kg) halved

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

Keep every other input at its default and halve the mass (kg). See how g (m/s²) responds.

  1. 01New Mass (kg): 2.98600e+24
  2. 02Baseline g (m/s²): 9.81953
  3. 03New g (m/s²): 4.90977
  4. 04g (m/s²) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Mass (kg) doubled

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

Keep every other input at its default and double the mass (kg). See how g (m/s²) responds.

  1. 01New Mass (kg): 1.19440e+25
  2. 02Baseline g (m/s²): 9.81953
  3. 03New g (m/s²): 19.6391
  4. 04g (m/s²) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Radius (m) halved

r = 3185500 (from 6371000)

Keep every other input at its default and halve the radius (m). See how g (m/s²) responds.

  1. 01New Radius (m): 3185500
  2. 02Baseline g (m/s²): 9.81953
  3. 03New g (m/s²): 39.2781
  4. 04g (m/s²) increases by 300% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Radius (m) doubled

r = 12742000 (from 6371000)

Keep every other input at its default and double the radius (m). See how g (m/s²) responds.

  1. 01New Radius (m): 12742000
  2. 02Baseline g (m/s²): 9.81953
  3. 03New g (m/s²): 2.45488
  4. 04g (m/s²) decreases by 75% → 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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