What formula does this calculator use?

It uses h = v² · sin²(θ) / (2g), where v is the initial speed, θ is the launch angle above horizontal, and g is gravitational acceleration (9.81 m/s² or 32.174 ft/s²). This comes directly from the kinematic equation v² = u² − 2as at the apex where vertical velocity is zero.

Which angle gives the greatest maximum height?

A 90° launch angle (straight up) gives the greatest maximum height for a given initial speed, because all of the velocity is in the vertical direction. At 0° the projectile travels horizontally with zero height gain.

Does air resistance affect this result?

This calculator assumes no air resistance (ideal conditions). In reality, drag reduces the maximum height, especially at high velocities. For most classroom and introductory physics problems, the ideal formula is sufficient.

Why is height zero when the angle is 0°?

At 0°, sin(0°) = 0, so the vertical component of the initial velocity is zero. The projectile is launched horizontally and immediately begins falling — it reaches no height above its launch point in this model.

How is this different from the projectile range formula?

Maximum height uses the vertical velocity component only (v·sinθ), while horizontal range uses the full formula R = v²·sin(2θ)/g. Range is maximized at 45°, whereas height is maximized at 90°.

Can I use this for imperial units (feet)?

Yes. Switch the unit selector to imperial (ft/s) and the calculator automatically uses g = 32.174 ft/s². The height result is then returned in feet.

Maximum Height Projectile Calculator

Name: Maximum Height Projectile Calculator
Availability: InStock
Author: Nham Vu

Enter initial velocity and launch angle to instantly calculate the maximum height a projectile reaches.

Launch Parameters

Unit System

Metric (m/s, m) Imperial (ft/s, ft)

Initial Velocity (m/s)

Speed of the projectile at the moment of launch.

Launch Angle (degrees)

Angle above horizontal (0° = flat, 90° = straight up).

Result

Enter values and press Calculate.

Formula Reference

h = v² · sin²(θ) / (2g)

h — maximum height above launch point
v — initial speed at launch
θ — launch angle above horizontal
g — gravitational acceleration (9.81 m/s² or 32.174 ft/s²)

Summary

Enter initial velocity and launch angle to instantly calculate the maximum height a projectile reaches.

How it works

Enter the initial launch velocity in meters per second (m/s) or feet per second (ft/s).
Enter the launch angle in degrees, measured from the horizontal (0° = flat, 90° = straight up).
Select the unit system — metric uses g = 9.81 m/s², imperial uses g = 32.174 ft/s².
The calculator applies h = v² · sin²(θ) / (2g) to find the maximum height.
The vertical velocity component at apex is always zero, confirming the peak.
Results update in real time as you adjust any input.

Use cases

Physics homework and exam problems on projectile motion.
Verifying manual kinematic equation solutions quickly.
Demonstrating how launch angle affects peak height in a classroom.
Sports science estimates for ball trajectories in basketball or football.
Engineering or ballistics rough-order-of-magnitude height checks.
Understanding why a 90° launch angle maximizes height for a given speed.
Comparing metric and imperial results side by side.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu