Projectile Motion and Range Calculator
Works out where a projectile lands and how high it goes.
Range
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
Maximum height above the landing point —
Time of flight —
Time to maximum height —
Landing speed —
Flight path, in metres
Reading this —
The formula
range on level ground = v² sin(2θ) ÷ g t = (v sinθ + √((v sinθ)² + 2gh)) ÷ g maximum height = h + (v sinθ)² ÷ 2g
Horizontal speed stays constant, and the vertical speed changes at g. Heights are measured from the landing point. The landing speed depends only on launch speed and height, not on the angle.
What to watch out for
Set the launch height to zero for level ground, which gives the textbook range formula.
Frequently Asked Questions
What angle gives the longest range?
45° on level ground, ignoring drag. From a raised launch it is lower: at 20 m/s from 10 m up, 45° reaches 49.1 m and 40° reaches 49.78 m.
How far does a 20 m/s throw at 45° go?
40.79 m, peaking at 10.2 m.