Kinematics Calculators

These 29 kinematics calculators solve motion problems, from projectile motion and free fall to displacement, momentum and friction. Each one shows its formula, names the published source, and gives answers in SI and US customary units.

What you can calculate

Projectile motion
Free fall
Displacement
Velocity
Acceleration
Momentum
Friction
Inclined plane

Arrow Speed CalculatorArrow Speed Calculator finds arrow fps from an IBO rating, draw length and arrow weight, with its kinetic energy, drop…Ballistic Coefficient CalculatorBallistic Coefficient Calculator finds a G1 or G7 BC from bullet weight, diameter and form factor, or from two velocities,…Car Jump Distance CalculatorCar Jump Distance Calculator finds how far a car flies off a ramp from its speed, ramp angle and heights,…Conservation of Momentum CalculatorConservation of Momentum Calculator finds final velocity, mass, kinetic energy lost and impulse in elastic, partially elastic or inelastic collisions.Displacement CalculatorDisplacement Calculator works from initial velocity, final velocity, acceleration and time, or totals velocity legs and north, south, east and…Free Fall CalculatorFree Fall Calculator gives fall distance, fall time and impact velocity from one known value, with air resistance, terminal velocity…Free Fall with Air Resistance CalculatorFree Fall with Air Resistance Calculator gives the fall time, impact velocity, terminal velocity and drag force from mass, shape,…Friction CalculatorFriction Calculator gives static and kinetic friction force, slip angle and acceleration from surfaces, load and slope, plus the coefficient…Ground Speed CalculatorGround Speed Calculator gives the ground speed, true heading and drift correction for a flight, or the speed in knots…Horizontal Projectile Motion CalculatorHorizontal Projectile Motion Calculator gives the range, flight time and impact speed of a level launch, or the launch velocity…Impulse and Momentum CalculatorImpulse and Momentum Calculator finds the impulse, final velocity and force in a hit, a kick or a push, from…Inclined Plane CalculatorInclined Plane Calculator gives the acceleration, forces, final speed and mechanical advantage of a block or a rolling object on…Magnitude of Acceleration CalculatorMagnitude of Acceleration Calculator finds the size of an acceleration from its x, y and z parts, velocity and time,…Maximum Height CalculatorMaximum Height Calculator finds the peak height of a projectile from its launch speed, angle and height, with time to…MOA CalculatorMOA Calculator converts minutes of angle to inches at any range, gives the angle of a group or a miss,…Momentum CalculatorMomentum Calculator finds p = mv for any object, solves for its mass or velocity, totals several objects, and lists…Muzzle Velocity CalculatorMuzzle Velocity Calculator gives bullet speed from its energy and weight, a timed distance or the barrel pressure, and lists…Polar Moment of Inertia CalculatorPolar Moment of Inertia Calculator finds J for a solid shaft, pipe, rectangle, ellipse or triangle, plus shear stress and…Projectile Motion CalculatorProjectile Motion Calculator finds the range, flight time and peak height of a launch, the angle or speed to hit…Projectile Range CalculatorProjectile Range Calculator finds how far a projectile travels from its speed, angle and height, on flat ground or a…Quarter Mile CalculatorQuarter Mile Calculator estimates the ET and trap speed of a car from its weight and power, or the power…Resultant Velocity CalculatorResultant Velocity Calculator adds up to five velocity vectors, gives the size and direction of the result, and solves a…Rolling Resistance CalculatorRolling Resistance Calculator finds rolling resistance force from mass and a coefficient, or a coefficient from tire pressure, with power…Sled Ride CalculatorSled Ride Calculator finds the speed of a sled at the foot of a hill from its angle, length and…SUVAT CalculatorSUVAT Calculator finds any two of displacement, initial velocity, final velocity, acceleration and time from the other three, with all…Terminal Velocity CalculatorTerminal Velocity Calculator finds the top speed of a falling object from mass, area, drag coefficient and air density, with…Time of Flight CalculatorTime of Flight Calculator finds how long a projectile stays in the air from launch speed, angle and height, or…Trajectory CalculatorTrajectory Calculator gives the path formula of a projectile, its height at any distance, the range and peak, and the…Velocity CalculatorVelocity Calculator finds velocity from distance and time, from acceleration, as an average over several legs, or from the flow…

What the Kinematics Calculators Cover

Kinematics describes motion through position, velocity, acceleration and time, without asking what causes it. The kinematics calculators in this hub are grouped by the kind of problem they solve, so you can match your question to a group first.

Problem type	What you can solve
Straight-line motion	Velocity, displacement, acceleration and time under constant acceleration, plus two velocities added as vectors.
Falling objects	Fall time, drop height and impact speed, with or without air resistance, and terminal velocity.
Projectile motion	Range, maximum height, time of flight and the full path, for angled and horizontal launches.
Momentum and collisions	Momentum, impulse, and the velocities of two objects after they collide.
Friction and slopes	Friction force, rolling resistance, and motion down an inclined plane.
Ballistics and archery	Muzzle velocity, ballistic coefficient, minute of angle and arrow speed.
Vehicles	Quarter-mile time and the distance a car covers off a ramp.

The Four Kinematic Equations

The straight-line, free fall and projectile kinematics calculators all run on the same four equations. They link five quantities, and each equation leaves exactly one of them out. The versions below follow OpenStax University Physics, section 3.4.

Equation	Leaves out	Reach for it when
v = u + at	Displacement, s	The problem gives a time and never mentions distance.
s = ut + ½at²	Final velocity, v	You know how the motion starts and how long it lasts.
v² = u² + 2as	Time, t	No time is given and none is asked for.
s = ½(u + v)t	Acceleration, a	Both velocities are known but the acceleration is not.

Here s is displacement, u is initial velocity, v is final velocity, a is acceleration and t is time. US textbooks often write the same equations with Δx for displacement and v₀ for initial velocity. The physics is identical, and only the letters change.

To pick an equation, mark the three quantities you know and the one you want. The fifth quantity is the one the problem never mentions, so use the equation that leaves it out. All four assume the acceleration stays constant for the whole interval.

Clues Hidden in the Wording

Many problems seem to give only two numbers, and the third is hidden in a phrase. Check for these phrases before you enter numbers into any of the kinematics calculators.

The problem says	It means
Starts from rest	u = 0
Comes to a stop	v = 0
Is dropped or released	u = 0, and a = g pointing down
Reaches its highest point	Vertical velocity = 0 at that instant
Moves at constant speed in a straight line	a = 0
Is thrown horizontally	Initial vertical velocity = 0
Lands at the height it was launched from	Vertical displacement = 0

Projectile Motion Formulas

A projectile keeps a constant horizontal velocity while its vertical velocity changes at the rate g. For a launch speed v₀ at an angle θ above the horizontal, three results follow from OpenStax University Physics, section 4.3.

Time of flight: T = 2v₀ sin θ / g

Range: R = v₀² sin 2θ / g

Maximum height: H = v₀² sin² θ / (2g)

A ball launched at 20 m/s and 30° stays in the air for 2.04 s, lands 35.3 m away and peaks at 5.10 m. The time of flight and range formulas only hold when the projectile lands at its launch height, and all three ignore air resistance.

Which Value of g to Use

The kinematics calculators here use standard gravity, g = 9.80665 m/s², which equals 32.174 ft/s². NIST lists this value as exact, because it is a defined standard and not a measurement.

Many textbooks round g to 9.8 or 9.81 m/s², which differ from the standard by 0.07% and 0.03%. If your answer and the book answer disagree in the third or fourth digit, the rounding of g is the usual reason.

Kinematics FAQ

Do the kinematic equations work when acceleration changes?

No. All four equations assume one constant acceleration, and the kinematics calculators built on them share that limit. If the acceleration changes in steps, split the motion into stages. The final velocity of one stage becomes the initial velocity of the next.

If the acceleration changes smoothly, the equations fail and calculus takes over. A falling object with air drag is the common case, because drag grows as speed grows. That is why free fall with air resistance is handled separately from plain free fall.

Why is my velocity or displacement negative?

A negative sign shows direction, not an error. You choose which direction is positive, and every quantity in the problem must follow that choice. With up as positive, gravity enters as a = −9.80665 m/s².

Take a ball thrown upward at 15 m/s. After 2 s its velocity is 15 − 9.80665 × 2 = −4.61 m/s. The ball has passed its peak and is moving down at 4.61 m/s. A negative displacement means it is below the starting point.

Does a heavier object fall faster?

Without air resistance, no. Mass cancels out of the free fall equations. Any object dropped from 20 m lands after 2.02 s at 19.8 m/s, whether it weighs one gram or one ton.

In real air the answer changes. Drag depends on shape and size, while weight depends on mass. A heavier object of the same shape has a higher terminal velocity, so it does fall faster over a long drop.