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Projectile Range Calculator

Range, maximum height and flight time for a projectile on flat ground.

By CalcHub Editorial · Last reviewed

Quick answer

  • Formula: Range = v² sin(2θ) ÷ g; Height = (v sinθ)² ÷ 2g; Time = 2v sinθ ÷ g
  • Worked example — Range: 40.7886 m (full example below).

Projectile Range Calculator

Worked example result
Range40.7886 m
Maximum height10.1972 m
Flight time2.8842 s

Launched at 20 m/s and 45°, a projectile travels about 40.79 m, peaks at 10.20 m and lands after 2.88 s.

Diagram: how the Projectile Range Calculator works — you enter Initial velocity, Launch angle; it applies the formula Range = v² sin(2θ) ÷ g; Height = (v sinθ)² ÷ 2g; Time = 2v sinθ ÷ g; and the worked example gives Range: 40.7886 m.
How the Projectile Range Calculator works — the inputs, the formula, and a worked example (Range: 40.7886 m).

A projectile launched at an angle follows a parabolic path under gravity alone. From the launch speed and angle this calculator finds how far it travels, how high it rises and how long it stays in the air.

Assumptions: flat ground, launch and landing at the same height, no air resistance, and g = 9.80665 m/s². Real objects with drag travel noticeably shorter, especially light or fast ones.

The formula

Range = v² sin(2θ) ÷ g; Height = (v sinθ)² ÷ 2g; Time = 2v sinθ ÷ g

Worked example

Launched at 20 m/s and 45°, a projectile travels about 40.79 m, peaks at 10.20 m and lands after 2.88 s.

Worked example for the Projectile Range Calculator: with Initial velocity 20, Launch angle 45, the result is Range: 40.7886 m; Maximum height: 10.1972 m.
The worked example, with the example values entered and the results they give.

The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.

Frequently asked questions

Which angle gives the maximum range?

45° on flat ground without air resistance — sin(2θ) peaks at θ = 45°. Angles equally above and below 45° (for example 30° and 60°) give the same range.

Why do real projectiles fall short of this?

Air resistance (drag) opposes the motion and is ignored here. Drag matters more for light, large or very fast objects; for a dense ball at modest speed the vacuum result is a good first estimate.

Category: Science calculators

Sources & methodology

This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.

Content last reviewed by CalcHub Editorial.

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