Projectile Motion Calculator
Calculate projectile motion instantly in your browser — the published formula, worked locally with no data sent anywhere.
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What this tool does
Calculate projectile motion instantly in your browser — the published formula, worked locally with no data sent anywhere. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
How to use the Projectile Motion Calculator
- Enter or select launch speed (m/s).
- Enter or select launch angle (degrees).
- Enter or select launch height (m).
- Read the calculated result; change any measurement to compare alternatives.
Formula
Resolve the launch velocity: vx = v·cos θ, vy = v·sin θ. Flight time solves h + vy·t − ½·g·t² = 0; range = vx × flight time; peak height = h + vy²/(2g), with g = 9.80665 m/s².
- speed
- Launch speed (m/s)
- angle
- Launch angle (degrees)
- height
- Launch height (m)
Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
Worked example
For projectile motion calculator, the following measurements illustrate the exact method: Launch speed (m/s): 20; Launch angle (degrees): 45; Launch height (m): 0.
Inputs
- Launch speed (m/s)20
- Launch angle (degrees)45
- Launch height (m)0
Result
- Range (m)40.79
- Range (ft)133.82
- Flight time (s)2.88
- Maximum height (m)10.2
- Impact velocity (m/s)20
- Horizontal velocity (m/s)14.14
- Initial vertical velocity (m/s)14.14
Results explained
- Range (m)
- Range (m) from the formula above. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
- Range (ft)
- Range (ft) from the formula above. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
- Flight time (s)
- Flight time (s) from the formula above. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
- Maximum height (m)
- Maximum height (m) from the formula above. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
- Impact velocity (m/s)
- Impact velocity (m/s) from the formula above. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
- Horizontal velocity (m/s)
- Horizontal velocity (m/s) from the formula above. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
- Initial vertical velocity (m/s)
- Initial vertical velocity (m/s) from the formula above. Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
Frequently asked questions
Resolve the launch velocity: vx = v·cos θ, vy = v·sin θ. Flight time solves h + vy·t − ½·g·t² = 0; range = vx × flight time; peak height = h + vy²/(2g), with g = 9.80665 m/s².
Vacuum trajectory — no air resistance, flat ground at height 0, constant g. Real projectiles (balls, shells) fall short of the vacuum range, increasingly so at high speed.
Range is proportional to sin(2θ), which peaks at θ = 45° when launch and landing heights are equal. From a raised launch the optimum drops slightly below 45°, because extra flight time from the height rewards a flatter throw.
Every field is labelled with its unit — enter values in exactly the labelled unit and read the result in the labelled output unit. Fields with a unit symbol also support the site-wide imperial/metric switch, which converts before the formula runs.
It uses double-precision arithmetic and the published constants and formulas named on this page. The last displayed digit may be rounded, and real conditions can differ from the idealized model described in the assumptions.
Yes. Every calculation runs entirely in your browser; nothing you enter is uploaded, stored or shared.