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Physics Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

Projectile Motion Calculator

You can calculate projectile flight time, horizontal range, maximum height, velocity components and impact speed from an initial speed, launch angle and optional launch height, with the trajectory plotted.

Runs in your browserFree · No sign-up · No watermark
v₀, θ → rangeRuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
v₀, θ → range
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Physics Tools

About Projectile Motion Calculator

Projectile motion is two simple motions stacked together. Horizontally the object keeps a constant velocity, while vertically it accelerates downward under gravity. Splitting the launch velocity into cosine and sine components is the step that makes every other quantity — flight time, apex height, range and impact speed — a matter of one formula each.

This calculator takes the initial speed, launch angle, optional launch height and gravity, then reports the components and the full flight, with a sampled trajectory plot to show the shape. It uses the ideal model: no air resistance, flat ground and constant gravity, so real throws travel a little shorter and land a little slower.

What this tool does

The details that matter when you use Projectile Motion Calculator for real work.

  • All flight quantities in one view

    Horizontal and vertical velocity components, time of flight, maximum height, range and impact speed are reported together.

  • Launch height supported

    Set the release height above the ground; the time-of-flight equation includes it instead of assuming a level launch.

  • Editable gravity

    Use 9.81 m/s² on Earth or change it for another planet or a textbook problem.

  • Trajectory plot

    An SVG plot sampled across the flight shows the path, the apex marker and the horizontal distance.

  • Formula and substitution

    Each result lists the equation with the values substituted, including the full time-of-flight form with h₀.

  • Assumption stated

    The ideal model (no drag, flat ground, constant gravity) is stated on the page, so the difference from real data is clear.

How to use Projectile Motion Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Enter the launch speed

    Use the initial speed in meters per second, along the launch direction.

  2. 02

    Set the angle and height

    Choose a launch angle between 0 and 90 degrees above the horizontal, and a release height of zero or more meters.

  3. 03

    Adjust gravity if needed

    The default is 9.81 m/s²; change it for the Moon, another planet or a simplified textbook value.

  4. 04

    Read the components and flight values

    The cards list horizontal and vertical velocity, flight time, maximum height, range and impact speed.

  5. 05

    Check the plot and formulas

    The trajectory plot shows the shape of the flight, and the formula panel substitutes your values into each equation.

How this tool works

Works with
v₀, θ → range
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • Ideal model only: air resistance, wind and the curvature of the Earth are not modelled.
  • Assumes a flat landing surface at a constant height below the launch point and constant gravity.
  • Angles are limited to 0–90 degrees above the horizontal; downhill or backward launches are not covered.

Privacy and file handling

Launch values are processed entirely in your browser. Nothing is uploaded, stored or logged, and the trajectory plot is generated locally as SVG.

Read the full privacy policy

Projectile Motion Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
What is projectile motion?
Projectile motion is the two-dimensional motion of an object moving under gravity alone after being launched. The horizontal velocity stays constant while the vertical velocity changes by g every second, so the path is a parabola when air resistance is ignored.
Which launch angle gives the maximum range?
On level ground without air resistance, 45 degrees maximizes the range. Two angles that add up to 90 degrees, such as 30 and 60 degrees, give the same range with different flight times and peak heights. With air resistance the best angle is usually a few degrees lower.
Why does the calculator ask for an initial height?
A projectile released above the ground stays in the air longer and travels farther than one launched from ground level at the same speed and angle. The time-of-flight equation adds the 2g·h₀ term under the square root, so the launch height is not simply ignored or added at the end.
What is time of flight in projectile motion?
Time of flight is the total time between launch and the moment the projectile returns to the ground. For a launch from height h₀ it is (vy + √(vy² + 2g·h₀)) ÷ g, where vy is the vertical component. The formula reduces to 2vy ÷ g when the launch is from ground level.
How is the maximum height of a projectile calculated?
The projectile is highest when its vertical velocity reaches zero, which happens vy ÷ g seconds after launch. The height at that moment is h₀ + vy² ÷ (2g). A launch at 0 degrees has no upward motion, so its maximum height is simply the release height.
Why can the impact speed be higher than the launch speed?
When a projectile is released above the ground, gravity keeps adding vertical speed during the extra fall. Energy conservation gives an impact speed of √(v₀² + 2g·h₀), which is larger than the launch speed whenever h₀ is greater than zero.
Does air resistance change the calculated range?
Yes. This calculator uses the ideal no-drag model, so a real ball or arrow falls short of the computed range, loses height earlier and lands at a steeper angle. The difference grows with speed and with the surface area of the object, which is why the page states the assumption clearly.
Can I calculate a ball thrown straight up?
Yes. Set the launch angle to 90 degrees: the horizontal velocity becomes zero, the range is zero and the flight time covers the rise and fall. The maximum height above the launch point is vy² ÷ (2g), and with a launch height the full time-of-flight formula still applies.

Background reading

Format guides that explain the trade-offs behind Projectile Motion Calculator.