What angle gives the maximum range?

A launch angle of 45 degrees gives the maximum horizontal range on flat ground with no air resistance. Angles above or below 45° (symmetric pairs like 30° and 60°) produce the same range but different heights and flight times.

Does this account for air resistance?

No. The calculator uses ideal kinematic equations that assume a vacuum environment and negligible air drag. Real-world ranges will be shorter due to air resistance, especially at high speeds.

What does "time of flight" mean?

Time of flight is the total duration from launch until the projectile returns to the same vertical height as the launch point (ground level). It equals T = 2v·sin(θ)/g.

Why is maximum height reached at half the flight time?

Because the vertical component of velocity decreases symmetrically due to gravity. The projectile decelerates going up at the same rate it accelerates coming down, so the apex is exactly halfway through the flight.

Can I enter 0° or 90° as the angle?

At 0° the projectile travels horizontally with no vertical lift, giving zero range and zero height from this model (pure horizontal shot). At 90° all velocity is vertical, so horizontal range is zero and the projectile goes straight up and comes straight down.

Range of Projectile Calculator

Name: Range of Projectile Calculator
Availability: InStock
Author: Nham Vu

Enter initial velocity and launch angle to instantly get horizontal range, max height, and time of flight for any projectile.

Projectile Inputs

Unit System

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

Initial Velocity (m/s)

Speed at the moment of launch

Launch Angle (degrees)

0° = horizontal · 45° = max range · 90° = straight up

Gravitational Acceleration (m/s²)

Horizontal Range

— m

R = v² · sin(2θ) / g

Maximum Height

— m

H = v² · sin²(θ) / (2g)

Time of Flight

— s

T = 2v · sin(θ) / g

Trajectory

Parabolic path (no air resistance)

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Summary

Enter initial velocity and launch angle to instantly get horizontal range, max height, and time of flight for any projectile.

How it works

Enter the initial velocity (speed at launch) in meters per second or feet per second.
Set the launch angle in degrees (0° is horizontal, 90° is straight up).
Select your preferred unit system (metric or imperial).
The calculator applies R = v²sin(2θ)/g, H = v²sin²(θ)/(2g), and T = 2v·sin(θ)/g.
Results for range, max height, and flight time appear instantly.
Use the trajectory chart to visualize the parabolic path of the projectile.

Use cases

Physics homework and exam preparation on projectile motion.
Checking manual kinematic equation solutions.
Demonstrating how launch angle affects range (45° gives maximum range).
Engineering ballistics or sports science estimates.
Teaching the relationship between angle, speed, and trajectory shape.
Comparing metric and imperial results side by side.

Frequently Asked Questions

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