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Escape Velocity Calculator — v = √(2GM/r)

v = √(2GM/r) — escape + orbital velocity for any planet, moon or star, in m/s, km/s and mph — browser-only

  • Runs locally
  • Category Calculator
  • Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.
kg
m
Body presetSpeed unitG = 6.674e-11 N·m²/kg²
Escape velocity11.186 km/s
Orbital velocity (first cosmic)7.9095 km/s

v_escape = √2 × v_orbit ≈ 1.414 × v_orbit

Formula steps

  1. v = √(2·G·M / r)
  2. v = √((2 × 6.674e-11 × 5.9720e+24) / 6,371,000)
  3. v = √(1.2512e+8)
  4. v_escape = 11,186 m/s
  5. v_orbit = 7,909.5 m/s = v_escape / √2

What this tool does

Free escape velocity calculator that turns a body mass and radius into the speed needed to leave its gravity for good. The formula is v = √(2GM/r), where G is the gravitational constant 6.674e-11, M the mass in kilograms and r the radius in metres. Type Earth (5.972e24 kg, 6.371e6 m) and you get the textbook 11.2 km/s; pick the Moon and it drops to about 2.38 km/s because the Moon holds less mass over a smaller radius. The tool also reports the orbital velocity, the first cosmic velocity √(GM/r) that keeps a satellite circling at the surface, and shows on screen that escape velocity is always exactly √2 times larger. One-click presets cover Earth, the Moon, Mars, the Sun and Jupiter, results switch between metres per second, kilometres per second and miles per hour, and every step of the square-root math is laid out so you can check the work. Everything runs in your browser with a shareable link that reopens the exact body. 100% client-side, no upload.

Tool details

Input
Numbers
The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output
Live result + Copy
The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy
Browser-side processing
The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share
Shareable URL state
Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget
Initial JS <= 9 KB
No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit
Calculator · Student
Category and role tags drive related tools, internal links, and quick fit checks.

How to use

  1. 1. Input

    Paste or drop your content into the tool panel.

  2. 2. Process

    Click the button. All processing is local in your browser.

  3. 3. Copy / Download

    Copy the result or download to disk in one click.

How Escape Velocity Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

  • Getting a realistic range before a purchase, plan, workout, or schedule decision.
  • Comparing scenarios by changing one input at a time.
  • Turning rough assumptions into a number you can discuss.

Calculation checks

  • Double-check units, dates, rates, and rounding assumptions.
  • Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
  • Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

  1. 1 Gravitational Force Calculator F = G·m1·m2 / r² · solve for force, distance or mass · scientific notation · Earth/Moon/Sun presets · 100% browser-only Open
  2. 2 Scientific Calculator Scientific calculator — sin / cos / log / sqrt / power, with full keyboard input + history, deg/rad mode. Open
  3. 3 Unit Converter Convert between length, weight, temperature, area, volume, speed, time — instant, browser-only Open

FAQ

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Made by Toolora · 100% client-side · Updated 2026-05-30