Introduction
Velocity tells you how fast something moves and in what direction. It is one of the most important ideas in physics. Whether a car speeds up on a highway, a ball falls from a roof, or a plane flies across the sky, velocity helps you describe that motion with numbers.
This velocity calculator lets you solve for velocity, distance, time, or acceleration using six different modes. You can use the basic formula v = d / t, work with kinematic equations like v = u + at and v² = u² + 2aΔx, find the average velocity across multiple trip segments, compute instantaneous velocity from a position function, or break a 2D velocity into its x and y components. Each mode shows a step-by-step solution so you can follow the math and learn as you go.
Just pick a mode, enter your known values, choose your units, and hit Calculate. The tool handles all unit conversions for you and displays results in both SI and your chosen units.
How to Use Our Velocity Calculator
Enter your known values into the fields and this velocity calculator will solve for the unknown. You can pick from six modes depending on which formula you need, and the tool will show your answer along with step-by-step work.
Choose a mode by clicking one of the tabs at the top. Each tab uses a different velocity formula. Pick the one that matches the values you already know.
v = d / t (Basic Mode)
Solve For lets you pick which value you want to find: velocity, distance, or time.
Distance (d) is how far the object travels. Type a number and choose a unit like meters, feet, or miles.
Velocity (v) is the speed of the object in a given direction. Pick a unit such as m/s, km/h, or mph.
Time (t) is how long the object moves. Choose a unit like seconds, minutes, or hours.
v = u + at (Acceleration with Time)
Solve For lets you pick the unknown: final velocity, initial velocity, acceleration, or time.
Final Velocity (v) is how fast the object moves at the end.
Initial Velocity (u) is how fast the object moves at the start. Set it to 0 if the object starts from rest.
Acceleration (a) is how quickly the speed changes. Use 9.8 m/s² for objects in free fall near Earth.
Time (t) is how long the acceleration lasts.
v² = u² + 2aΔx (No Time Needed)
Solve For lets you pick the unknown: final velocity, initial velocity, acceleration, or displacement.
Displacement (Δx) is the straight-line distance between the start and end points. This is not the same as total path length.
The other inputs (final velocity, initial velocity, and acceleration) work the same as in the previous mode.
Average Velocity (Multi-Segment)
Velocity and Time fields appear for each segment of a trip. Enter the speed and how long that speed was held for each part of the journey.
Click Add Segment to include more parts. Click the ✕ button to remove a segment. You must have at least two segments.
Instantaneous v(t)
Position function x(t) is a math expression that describes where the object is at any time t. For example, type 3t^2 - 2t + 1. You can use sin, cos, sqrt, and other common functions.
Evaluate at t₀ is the exact moment in time where you want to know the velocity.
Step size (h) controls how precise the calculation is. A smaller number gives a more accurate result. The default of 0.0001 works well in most cases.
Position unit sets the unit used in your x(t) expression, such as meters or feet.
2D Vector
Pick Component (vₓ, vᵧ) mode to enter the x and y parts of a velocity. The calculator will find the total speed and direction angle.
Pick Polar (|v|, θ) mode to enter a speed and angle. The calculator will break it into x and y components. You can switch between degrees and radians.
Precision and Output Settings
Significant Figures controls how many meaningful digits appear in the answer. Set it to Auto or choose a number from 3 to 9.
Fixed Decimals locks the answer to a set number of decimal places when turned on. Use the Decimal Places dropdown to pick how many.
Show Steps turns the step-by-step solution box on or off. Keep it on to see the full work behind each answer.
Press Calculate to get your result. Press Reset to clear all fields and start over.
What Is Velocity?
Velocity tells you how fast something moves and in what direction. If a car drives 60 miles per hour north, that is its velocity. Speed only tells you how fast, but velocity also tells you which way. This difference matters a lot in physics.
How to Calculate Velocity
The most basic velocity formula is v = d / t, which means velocity equals distance divided by time. If you walk 10 meters in 5 seconds, your velocity is 2 meters per second. This works when speed stays the same the whole time.
When speed changes, you need a different formula. The equation v = u + at finds your final velocity when you know your starting velocity (u), your acceleration (a), and how long you sped up or slowed down (t). For example, a ball dropped from rest speeds up at 9.8 m/s² due to gravity. After 3 seconds, it moves at 29.4 m/s.
The equation v² = u² + 2aΔx is useful when you do not know the time. It connects final velocity, starting velocity, acceleration, and distance traveled. This helps solve problems like finding how fast a car goes after speeding up over a known stretch of road.
Average Velocity vs. Instantaneous Velocity
Average velocity looks at a whole trip. If you drive 100 km in 2 hours, your average velocity is 50 km/h. It does not matter if you went faster or slower at different points along the way.
Instantaneous velocity is your velocity at one exact moment in time. It is what a speedometer shows. In math, it is found by taking the derivative of a position function. This calculator uses a method called the central difference to estimate that derivative. Because velocity is fundamentally a rate of change of position, this derivative approach gives the most precise answer at any given instant.
2D Velocity Vectors
Objects do not always move in a straight line. A kicked soccer ball moves both forward and upward at the same time. You can break this motion into two parts: an x-component (left-right) and a y-component (up-down). The full speed is found with the Pythagorean theorem: |v| = √(vx² + vy²). The direction angle is found using the arctangent function.
Common Velocity Units
Velocity is measured in distance per time. The most common units are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph). Scientists almost always use m/s. To convert km/h to m/s, divide by 3.6. To convert mph to m/s, multiply by 0.44704.
Related Calculations
Velocity connects to many other quantities in mechanics. Once you know an object's velocity, you can find its kinetic energy using ½mv² or its momentum using p = mv. If a force acts on the object, you can use Newton's second law to determine how the velocity will change.