how-to · 5 min read

How to use the projectile motion calculator: inputs, outputs and examples

The projectile motion calculator answers a specific question: if something is launched at a given speed and angle from a given height, where does it go and how long does it take? You supply the launch conditions, and the tool returns the velocity components, flight time, maximum height, horizontal range and impact speed, with an ideal path drawn from the same numbers.

This walkthrough explains what each input does, shows how to read the outputs, and works through two complete examples — a ground-level launch and the same launch from a height — before covering the degrees-versus-radians mistake and the reason real projectiles land shorter than the ideal model predicts.

By FormatFlow EditorialUpdated October 21, 2026More Physics Tools →

The four inputs and the units they expect

Initial speed is the magnitude of the launch velocity in meters per second. If the value you have is in kilometers per hour, divide by 3.6 first: 72 km/h is 20 m/s. The calculator does not convert this field, because velocity is the one quantity where the unit is part of the launch condition rather than a display preference.

The launch angle is measured in degrees above the horizontal, from 0 to 90. The calculator expects degrees, not radians, so 45 means 45 degrees. If you are computing the components in a spreadsheet, remember that spreadsheets' sine and cosine functions usually expect radians and need a conversion step, which is one of the most common sources of wrong trajectories.

Initial height is the vertical distance above the ground at launch, in meters, and defaults to 0 for a level surface. Gravity defaults to 9.81 m/s² for Earth but is editable, so the same tool works for the Moon, a planet in a textbook problem, or a simplified value your course uses.

What the outputs mean

The horizontal velocity vx stays constant throughout the flight in this model, while the vertical velocity vy starts at the launch value and decreases by g every second. Time of flight is the time until the projectile returns to ground level, and maximum height is the highest point above the ground, including the launch height when there is one.

Range is the horizontal distance traveled before landing. Impact speed combines the horizontal velocity with the vertical velocity at the moment of landing, so it is generally larger than the launch speed when the projectile falls from a height. The plot shows the same flight sampled across its duration, with a marker at the highest point.

Example one: 20 m/s at 45 degrees from the ground

Enter an initial speed of 20 m/s, an angle of 45 degrees and an initial height of 0. The components come out at about 14.14 m/s each, because the cosine and sine of 45 degrees are equal. The time of flight is about 2.88 seconds and the maximum height is about 10.19 meters.

The horizontal range is about 40.77 meters, and because the launch and landing heights are equal, the trajectory is symmetric and the impact speed equals the launch speed of 20 m/s at the same angle below the horizontal. These are ideal-model numbers for a projectile in a vacuum over a flat surface, which is the right comparison for a physics problem and only an estimate for the real world.

Example two: the same launch from 5 meters up

Raise the initial height to 5 m while keeping 20 m/s and 45 degrees. The horizontal and vertical launch components do not change, but the extra height keeps the projectile in the air longer: the time of flight becomes about 3.20 seconds. The maximum height rises to about 15.19 meters because the whole trajectory is lifted by the launch height.

The range increases to about 45.28 meters, since the projectile spends those extra fractions of a second moving horizontally at 14.14 m/s. The impact speed rises to about 22.32 m/s, which follows from the same energy argument as any fall from a height: the extra drop adds kinetic energy even though the launch speed is unchanged.

Degrees, radians and why real flights are shorter

The radians trap deserves its own warning. A 45-degree angle is about 0.785 radians, so entering 0.785 into a calculator that expects degrees produces a nearly horizontal launch and a completely different answer. When moving a calculation between the tool and a spreadsheet or programming language, check which unit the trigonometric function expects before copying numbers.

The other difference is physics rather than arithmetic. This model ignores air resistance, so real balls, arrows and projectiles lose horizontal speed and height as they travel, land shorter than the calculated range and descend more steeply than they rose. The ideal curve is still useful: it gives an upper estimate for range and a clear picture of which input matters most.

Frequently asked questions

Should I enter the launch angle in degrees or radians in the calculator?

Enter degrees, in the range 0 to 90. The field is labeled with the degree symbol, and 45 means 45 degrees above the horizontal. If you calculated the angle in radians elsewhere, multiply by 180 and divide by pi before entering it, or the trajectory will be misinterpreted.

Why is the horizontal velocity constant in the projectile model?

Gravity acts vertically, so in the absence of air resistance there is no horizontal force to change horizontal velocity. The vertical component changes by g every second while the horizontal component stays at v₀ × cos θ, which is why the path is a parabola and the two components can be handled separately.

What does changing the initial height do to the result?

A higher launch point keeps the projectile in the air longer at the same speed and angle, so the range grows and the impact speed can increase because of the extra fall. The maximum height is also measured above the ground, so it includes the launch height rather than measuring only the rise from the release point.

Why is the impact speed higher than the launch speed in the height example?

When the projectile lands lower than it started, gravity has added kinetic energy during the extra fall. The impact speed follows from energy conservation and equals the square root of the launch speed squared plus twice g times the drop height, which is why the 5 m launch lands at about 22.32 m/s instead of 20 m/s.

Why does the calculator's range differ from a real throw or shot?

The model assumes no air resistance, flat ground and constant gravity. Real projectiles experience drag that grows with speed, plus spin, wind and surface effects, so they lose range and height and land at a steeper angle. The calculated value is an upper estimate for comparison, not a prediction of a real launch.

Tools for this job

All Physics Tools