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Physics

Escape Velocity Calculator

v = √(2GM/r). Free online Escape Velocity Calculator. Calculate escape velocity online — fast, accurate, mobile-friendly, no signup needed.

v_esc = √(2·G·M/r).
v (m/s)
11,185.726492

Derivation

  1. ├── 01GivenM = 5.972e+24, r = 6371000
  2. ├── 02Formula√(1.3348e-10 × t / a)
  3. └── 03Compute v (m/s)11,185.726492
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§01What is

Understanding the Escape Velocity Calculator

The Escape Velocity Calculator computes v (m/s) from 2 inputs: body mass (kg), radius (m). v = √(2GM/r).

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 Escape Velocity Calculator sits in that toolkit — it v = √(2GM/r). 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

√(1.3348e-10 × t / a)

Where

M
Body mass (kg)
r
Radius (m)
§03Practical Example

Step-by-step walkthrough

Scenario

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

  1. 01Start by noting the input — Body mass (kg): 5.972e+24.
  2. 02Start by noting the input — Radius (m): 6371000.
  3. 03Substitute these values into the formula: √(1.3348e-10 × t / a)
  4. 04Compute v (m/s): the calculator returns 11185.7.
  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 Escape Velocity 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

Body mass (kg) halved

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

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

  1. 01New Body mass (kg): 2.98600e+24
  2. 02Baseline v (m/s): 11185.7
  3. 03New v (m/s): 7909.5
  4. 04v (m/s) decreases by 29.3% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Body mass (kg) doubled

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

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

  1. 01New Body mass (kg): 1.19440e+25
  2. 02Baseline v (m/s): 11185.7
  3. 03New v (m/s): 15819
  4. 04v (m/s) increases by 41.4% → 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 v (m/s) responds.

  1. 01New Radius (m): 3185500
  2. 02Baseline v (m/s): 11185.7
  3. 03New v (m/s): 15819
  4. 04v (m/s) increases by 41.4% → 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 v (m/s) responds.

  1. 01New Radius (m): 12742000
  2. 02Baseline v (m/s): 11185.7
  3. 03New v (m/s): 7909.5
  4. 04v (m/s) decreases by 29.3% → 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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