By Zencalcy Editorial TeamLast reviewed About us
The path of a projectile in a vacuum is a parabola. Given launch speed, angle and launch height, this calculator gives the height at any horizontal distance, which is useful for checking whether a shot clears an obstacle.
Height of a projectile at any horizontal distance.
y = h₀ + x tan θ − gx² / (2v²cos²θ)
A negative result means the projectile would have hit the ground before reaching that distance.
| Symbol | Meaning |
|---|---|
| v | Launch speed, in metres per second. |
| θ | Launch angle above the horizontal. |
| h₀ | Launch height, in metres. |
| x | Horizontal distance from launch, in metres. |
| y | Height at that distance, in metres. |
The projectile is 7.55 m high at 10 m from launch, on its way to a 10.20 m peak.
Continue with the Velocity Calculator, Magnitude of Acceleration Calculator, or the Arrow Speed Calculator — or browse more kinematics tools and all physics calculators.
The gravity term grows with the square of horizontal distance while the straight-line term grows linearly, so the parabola bends downward.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Content updated: September 2026