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Physics

Orbital Velocity Calculator

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

v_orb = √(G·M/r).
v (m/s)
7,672.317978

Derivation

  1. ├── 01GivenM = 5.972e+24, r = 6771000
  2. ├── 02Formula√(6674e-14 × t / a)
  3. └── 03Compute v (m/s)7,672.317978
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§01What is

Understanding the Orbital Velocity Calculator

The Orbital Velocity Calculator computes v (m/s) from 2 inputs: body mass (kg), orbit radius (m). v = √(GM/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 Orbital Velocity Calculator sits in that toolkit — it v = √(GM/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

√(6674e-14 × t / a)

Where

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

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Body mass (kg) = 5.972e+24, Orbit radius (m) = 6771000.

  1. 01Start by noting the input — Body mass (kg): 5.972e+24.
  2. 02Start by noting the input — Orbit radius (m): 6771000.
  3. 03Substitute these values into the formula: √(6674e-14 × t / a)
  4. 04Compute v (m/s): the calculator returns 7672.32.
  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 Orbital 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): 7672.32
  3. 03New v (m/s): 5425.15
  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): 7672.32
  3. 03New v (m/s): 10850.3
  4. 04v (m/s) increases by 41.4% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Orbit radius (m) halved

r = 3385500 (from 6771000)

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

  1. 01New Orbit radius (m): 3385500
  2. 02Baseline v (m/s): 7672.32
  3. 03New v (m/s): 10850.3
  4. 04v (m/s) increases by 41.4% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Orbit radius (m) doubled

r = 13542000 (from 6771000)

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

  1. 01New Orbit radius (m): 13542000
  2. 02Baseline v (m/s): 7672.32
  3. 03New v (m/s): 5425.15
  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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