Orbital Velocity
v = √(GM/r) for a circular orbit
Orbital Velocity is built for v = √(GM/r) for a circular orbit — fast, free, and private. You provide Central Mass (kg) and Altitude (km); the tool does the rest in real time. The result comes with a step-by-step breakdown — no black box, just math you can check. Great when you want certainty fast — no formulas to memorize, no apps to install. Your inputs never leave your device: the calculation is fully client-side, and optional analytics/advertising only activate with your consent. It is part of the Science collection on CalcProMaster, alongside orbital velocity calculator satellite earth, free online orbital velocity calculator and more. It is one of the fastest ways to get from question to answer without a spreadsheet. Bookmark it and the answer is always one click away.
What does the Orbital Velocity do?
Orbital Velocity works out the √(gm/r) from the Central Mass and Altitude, following standard Science conventions — the page defaults produce a √(gm/r) of v = 7671.03 m/s.
- Inputs: Central Mass and Altitude.
- Output: the √(gm/r), plus the intermediate steps behind it.
- Method: the standard Science formula, evaluated entirely in your browser.
Quick answer
With the default inputs (central mass of 5,970,000,000,000,000,000,000,000, altitude of 400), orbital velocity returns a √(gm/r) of v = 7671.03 m/s. Assumptions and limits are summarized below.
How does the Orbital Velocity work?
Orbital Velocity computes the √(gm/r) directly from your inputs — the Central Mass and Altitude feed the formula. Nothing is uploaded: the math runs locally in your browser and the result appears as you type.
How it works
This page is a working orbital velocity: enter your values, read the √(gm/r), and follow the step list to see exactly how the answer was derived.
How to use it
- Central Mass — one of the values the calculation builds from; the result reflects exactly what you type here.
- Altitude — used in the first stage of the calculation, so entering it accurately matters more than any later refinement.
- Note the √(gm/r). It updates as you type, and the worked steps below it make the arithmetic auditable.
- Adjust and re-run. Change one input at a time to see how sensitive the √(gm/r) is to it — the fastest way to understand what the calculation is doing.
The formula behind the result
Rounding follows standard display conventions — the underlying math keeps several decimal places until the √(gm/r) is shown.
Worked example: with central mass of 5,970,000,000,000,000,000,000,000, altitude of 400, this orbital velocity calculation returns v = 7671.03 m/s. The same run reports Period: 1.54 hours.
The steps it follows:
- r = R_earth + altitude = 6.771e+6 m
- v = √(GM/r) = 7671.03 m/s
- Period = 2πr/v = 1.54 h
Substitute your own values and the same steps produce your answer — that is the point of a calculator that shows its working.
Understanding the result
To interpret the result from orbital velocity, read it together with the intermediate figures — the pairing is what makes the number auditable.
Where it helps
Orbital Velocity fits planning and checking: planning and budgeting, comparing scenarios side by side, and double-checking the √(gm/r), or any moment when the √(gm/r) needs to be right the first time.
Common mistakes
Copying the √(gm/r) without its assumptions is the frequent error — the number is valid for exactly the inputs shown, so carry the context with it.
Tip: Run Orbital Velocity twice with deliberately low and high inputs; the spread tells you how sensitive the output is, which a single run never shows.
Assumptions and limitations
Results from Orbital Velocity are estimates computed from the values entered; real-world outcomes can differ when fees, taxes, or conditions not modeled here apply.
Why use this calculator
Because the page doubles as documentation: Orbital Velocity puts the formula, a worked example, and the assumptions right beside the calculator.
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Frequently Asked Questions
What does the Orbital Velocity calculate?
Orbital Velocity turns the values you enter into a verified result — the formula, every intermediate step, and the assumptions sit beside the result instead of hidden behind it. Because the working is visible: Orbital Velocity shows each operation behind the output in the steps panel, so you can verify the result instead of trusting a black box.
How is the √(gm/r) calculated?
The first steps are r = r_earth + altitude = 6.771e+6 m, then v = √(gm/r) = 7671.03 m/s. Orbital Velocity substitutes the Central Mass and Altitude into the formula, evaluates it in the order shown in the steps panel, and reports the √(gm/r) rounded for readability.
What do I need to use the Orbital Velocity?
The Central Mass and Altitude it asks for, or the page defaults if you just want to see the calculation work. Each input maps directly to the formula, and changing any one of them recalculates the √(gm/r) instantly.
What does the result from the Orbital Velocity mean?
The main number the orbital velocity returns is the √(gm/r) for your exact inputs, and the supporting figures and step list give it context. Inputs outside a reasonable range may produce a √(gm/r) that is mathematically correct but practically implausible; the steps panel helps you spot that quickly.
When is the Orbital Velocity most useful?
Typical uses for Orbital Velocity include planning and budgeting, comparing scenarios side by side, and double-checking the √(gm/r) — anywhere the figure needs to be defensible rather than guessed. On this page, orbital velocity applies the standard Science method to your inputs and lists every step of the working beside the result.