Projectile Motion Calculator (Range)
Projectile motion calculator: range, maximum height and flight time from launch speed and angle.
R = v² sin 2θg
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
On level ground and without air resistance, R = v²·sin 2θ / g. The longest range is at 45°.
Complementary angles (30° and 60°) give the same range.
Formula
R = v² sin 2θg
| Symbol | Quantity | Units |
|---|---|---|
| v0 | Launch speed | m/s, km/h, mph, kn, ft/s, c |
| θ | Launch angle | °, rad, gon, turn, ′, ″, mrad |
| R | Range (level ground) | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
Constants used: g = 9.80665 m/s²
Worked example
Given: v0 = 20 m/s · θ = 45 °
R = v² sin 2θg
Result: R = 40.7886 m
Frequently asked questions
Range at 20 m/s and 45°?
About 40.8 m, with a peak height of 10.2 m.