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Terminal Velocity Calculator

Calculates the terminal velocity of a falling object from its mass, drag coefficient and area, with the time and distance to reach it.

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Only the PRODUCT of this and the area is really constrained. A belly-down skydiver is about 0.49 m² all told.
Sea-level air is 1.225. Water is about 1000.
Enter your figures and press Calculate.
In short Terminal velocity is the speed at which drag exactly cancels weight, so the net force is zero and nothing accelerates further: v = √(2mg ÷ ρCdA). For an 80 kg skydiver with a drag area of 0.49 m² that is 51.1 m/s, or 184 km/h — the familiar belly-down figure. This page prints the drag force and the weight side by side at that speed so you can see them balance, because that balance IS the definition and the formula is only it rearranged. Two things surprise people. Terminal velocity is never actually reached: speed approaches it exponentially, arriving at 95% after 9.55 seconds and 310 m of fall, and never quite getting there. And the scaling is square-root, not linear — halving your drag area raises the speed by 41%, not 100%, and four times the mass only doubles it. That square root is why a heavy object falls faster in air even though mass cancels in a vacuum, and why a skydiver pulling into a tight position speeds up much less than it feels. The honest caveat is that the drag coefficient and the area are not separately knowable for an awkward shape like a person; only their product is constrained. Quoting a drag coefficient to two decimals while guessing the area is false precision, which is why the page reports the product.

How to use the Terminal Velocity Calculator

  1. Enter your figures in the input fields.
  2. The result updates as you type, together with the full working.
  3. Check the breakdown table to see exactly how the number was reached.

About the Terminal Velocity Calculator

The speed at which air resistance balances weight, and how long it takes to get there.

What people use it for

  • Estimating how fast a falling object ends up going.
  • Comparing a skydiver's belly-down and head-down speeds.
  • Seeing where the vacuum free-fall answer stops being usable.

Details

Belly-down skydiverabout 184 km/h at a drag area of 0.49 m²
Reaching 95% of it takes9.55 s and 310 m
Halving the drag arearaises the speed by 41.4%, not 100%
Four times the massexactly doubles it
At terminal velocitydrag force equals weight, exactly

The maths behind it

This tool uses v = √(2mg ÷ (ρ·Cd·A)), with speed over time following v(t) = v·tanh(gt ÷ v). Every intermediate value is shown on screen, so the result can be checked by hand.

The drag force and the weight are both printed at the computed speed. They must be equal, and seeing them match is a check the reader can run rather than a claim to accept.

Where this tool stops

This assumes a constant drag coefficient and constant air density, and neither holds over a long fall — the air thins with altitude, so a high-altitude jump starts much faster and slows as it descends. It also treats the object as falling straight down with a fixed orientation.

Frequently asked questions

Why does a heavier object fall faster in air but not in a vacuum?
In a vacuum mass cancels. In air, weight grows with mass while drag depends only on size and shape, so a heavier object needs more speed before the two balance. Terminal velocity goes as √m.
Is terminal velocity ever actually reached?
No. The approach is exponential, so it gets to 95% after about 9.5 seconds and closer forever after. "Terminal velocity" is a limit rather than a speed you arrive at.
What drag coefficient should I use?
For a person, use the product instead: about 0.49 m² belly-down and roughly half that head-down. Cd and area cannot be separated meaningfully for an irregular shape, and pretending otherwise gives false precision.
Does this work in water?
Yes — set the density to about 1000. The terminal velocity drops by a factor of roughly 28, which is √(1000/1.225), and it is reached almost immediately.
Is the Terminal Velocity Calculator free, or is there a paid tier?
It is free, with no account, no trial and no daily cap. Every calculators tool on inputtesthub.com works the same way: open the page and use it.
Is what I paste into the Terminal Velocity Calculator stored?
No. The Terminal Velocity Calculator runs entirely in your browser using JavaScript. Nothing is transmitted, logged or stored, which you can verify yourself in the Network tab of your browser's developer tools.
What is the equation behind the Terminal Velocity Calculator?
It uses v = √(2mg ÷ (ρ·Cd·A)), with speed over time following v(t) = v·tanh(gt ÷ v). The full working is printed under the result, so you can follow every step rather than trusting a black box.
What does a typical result look like?
Enter 80 kg, Cd 0.7, 0.7 m² and the Terminal Velocity Calculator returns 51.13 m/s, 184.1 km/h.
Who is the Terminal Velocity Calculator for?
The most common reasons people reach for it: estimating how fast a falling object ends up going. Comparing a skydiver's belly-down and head-down speeds. Seeing where the vacuum free-fall answer stops being usable. It is built for exactly those cases rather than being a general-purpose tool with this bolted on.
What are the limits of the Terminal Velocity Calculator?
This assumes a constant drag coefficient and constant air density, and neither holds over a long fall — the air thins with altitude, so a high-altitude jump starts much faster and slows as it descends. It also treats the object as falling straight down with a fixed orientation. Knowing where a tool stops being trustworthy matters more than the cases where it works.
What are the reference figures here?
Belly-down skydiver is about 184 km/h at a drag area of 0.49 m². Reaching 95% of it takes is 9.55 s and 310 m. Halving the drag area is raises the speed by 41.4%, not 100%. These are printed on the page itself, so you do not have to take them on trust.
Is the number rounded?
The calculation runs in double precision and the result is shown to ten significant figures, so converting a value and converting it back returns the original. What is displayed is rounded for readability; what is copied is not.

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