Velocity Calculator

Velocity is speed with a direction. Type the numbers you have and read the answer. There is no equation to pick first: fill in a start speed with an acceleration and a time, or swap the time for a displacement, and the calculator finds the route that works. Something dropped from rest for 3 seconds is falling at 29.41995 m/s, which is 105.9118 km/h, or 65.8106 mph — all three at once, because whichever unit the question is written in, you shouldn't have to convert it yourself afterwards. Under the answer it writes out the formula it used with your numbers substituted in, so you can copy the working and not just the result. Anything else it can pin down from what you gave it — the distance covered, the acceleration behind the change, the time it took — gets filled in and labelled, so one set of numbers answers more than the single question you arrived with. Displacement is signed here and a negative answer is kept as a negative answer, because in kinematics the minus sign is the direction and throwing it away is how a right answer turns into a wrong one two steps later. Most calculators for this make you choose a velocity formula from a dropdown before they will let you type anything, which means you have to already know which equation your problem is, and several of the ones that rank for this term quietly solve distance over time and call that velocity. This one takes the numbers you happen to have.

Built by Bob QA by Ben Shipped September 20, 2026

How to use

1
Type whatever you already know into the five boxes. The usual set is a start speed, an acceleration and a time. If you never timed it, give a displacement instead. If you have a displacement and a time but no acceleration, that works too.
2
Pick your units from the dropdowns. One velocity unit covers both the start speed and the final speed on purpose — mixing mph and m/s inside a single motion is the fastest way to get a confidently wrong answer. Switching a unit converts the number you already typed rather than reinterpreting it, so the answer never jumps.
3
Read the velocity. It shows in m/s large, with km/h and mph underneath. A negative reading is not an error: it means the motion is in the opposite direction to the one you called positive, and the tool tags it `Moving backward`. A reading of exactly zero is tagged `Stopped`.
4
Check the formula line under the result. It names the route used and substitutes your numbers, so `v = v₀ + a·t = 0 + 9.80665 × 3 = 29.41995 m/s` is the working, not just the answer.
5
Look at the fields marked `solved`. Those are values worked out from your numbers — a displacement you never measured, an acceleration you were not given. Fields marked `given` are the ones you typed.
6
If you only give a displacement and a time, the headline says `Average velocity` rather than velocity. That is deliberate: distance over time is the mean across the whole trip, not the speed at the end. Add an acceleration or a start speed to get the final velocity.
7
If you fill in two sets that contradict each other, the result hides and it tells you both numbers instead of quietly picking one. Clear one field and it comes back.
8
Hit Copy results for a three-line plain-text summary — the answer in all three units, the inputs you gave, and the formula — ready to paste into a lab report or a homework answer.

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Frequently asked questions

What is the formula for final velocity?

The one most people mean is v = v₀ + a·t: the start speed plus the acceleration multiplied by how long it acted. Drop something from rest and let gravity pull on it for 3 seconds and you get v = 0 + 9.80665 × 3 = 29.41995 m/s. There are three other routes to the same number and this tool checks all of them: v = √(v₀² + 2a·Δd) when you know the displacement but never timed it, v = 2Δd/t − v₀ when you know the displacement and the time but not the acceleration, and v̄ = Δd/t when displacement and time are genuinely all you have. They describe the same motion — which one applies depends only on which numbers you happen to have, which is why there is no formula picker on this page.

What's the difference between speed and velocity?

Speed is a magnitude; velocity is a magnitude plus a direction. Speed can only be zero or positive, so a car doing 30 mph in reverse has a speed of 30 mph and a velocity of −30 mph relative to forward. That sign matters as soon as you do anything else with the number: add two velocities and the signs cancel correctly, add two speeds and they don't. It's also why a lap of a running track can have a high average speed and an average velocity of exactly zero — you finish where you started, so the displacement is zero even though the distance was 400 m. This calculator keeps the sign throughout and treats a negative displacement as a real input rather than a typo.

How do I find final velocity without knowing the time?

Use the displacement. The identity v² = v₀² + 2a·Δd doesn't contain time at all, so a start speed, an acceleration and a distance are enough. Something starting from rest and accelerating at 2 m/s² over 100 m arrives at √(0² + 2 × 2 × 100) = 20 m/s. Enter those three numbers and leave the time box empty; the tool takes the √ route and then back-fills the time it must have taken, which in that example is 10 seconds. The root is chosen to match the direction you're already moving, so you never get handed a ± and left to decide which one your problem meant.

Why is my answer negative?

Because the motion ended up pointing the other way, and that's a real result rather than a mistake. A negative velocity means the object is moving opposite to whatever direction you treated as positive when you typed the numbers in. It shows up constantly in braking and free-fall problems: choose up as positive and everything falling has a negative velocity. The tool tags it `Moving backward` and keeps the sign rather than showing you an absolute value, because the sign is the direction and dropping it is what causes the answer to be wrong two steps later when you feed it into a momentum or energy calculation.

What's the difference between average velocity and final velocity?

Average velocity is the displacement divided by the time — it describes the whole trip as one number. Final velocity is how fast the object is going at the end of it. They only agree when the velocity never changed. Under constant acceleration the average is (v₀ + v)/2, which is why a car accelerating from a standstill to 20 m/s has an average of 10 m/s across the run but is doing 20 m/s at the finish line. If you give this tool only a displacement and a time it has no way to know how the speed was distributed, so it labels the headline `Average velocity` and says so, rather than presenting a mean as if it were the final answer.

What does 9.80665 m/s² mean, and when should I use it?

That's standard gravity — the internationally agreed value for the acceleration of a falling object near the Earth's surface, used as the definition of the unit `g`. Use it for any free-fall problem where air resistance is ignored, which is nearly all of them in an introductory course. Many textbooks round it to 9.8 or 9.81 m/s²; the difference reaches about 0.02 m/s after 3 seconds of falling, so it rarely changes an answer but it will change the last digit. You can type whichever value your course uses, or switch the acceleration unit to `g` and type 1. Real local gravity varies from roughly 9.764 to 9.834 m/s² depending on latitude and altitude.

Why does the tool sometimes hide the answer and show two numbers?

Because the numbers you typed describe two different motions and there is no honest way to pick one. If you enter a start speed, an acceleration and a time, that pins the final velocity. If you also enter a displacement, that pins it again — and if the two disagree by more than a rounding error, something in the inputs is wrong. Rather than silently preferring one route and handing you a plausible-looking number, the tool hides the result and prints both candidates so you can see which one matches the problem you meant. Clear whichever field doesn't belong and the answer comes straight back.

Can I use this for projectile motion or falling objects?

For the vertical part, yes — free fall is just constant acceleration with a = 9.80665 m/s² downward, so a dropped object or a ball thrown straight up is exactly what this solves. Full projectile motion with an angle is a different problem: you'd split the launch velocity into horizontal and vertical components and treat the vertical one here while the horizontal stays constant. This page deliberately doesn't do the angle for you, and it doesn't model air resistance, drag, or anything rotational. One job, one answer.

Does this work for constant speed with no acceleration?

Yes — enter an acceleration of 0 and the final velocity comes back equal to the start speed, which is the correct answer for something that isn't speeding up or slowing down. If what you actually want is travel planning — how long a drive takes at a given speed, or what speed covers a distance in a given time — that's the scalar v = d/t question, and the Speed Calculator is the right page for it. This one is built for kinematics under constant acceleration, where the direction is part of the answer.

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Velocity Calculator

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