Projectile Motion Calculator
Calculate a projectile's time of flight, maximum height, and horizontal range from its launch speed and angle.
This uses the standard idealized projectile motion model: no air resistance, and launch and landing at the same height.
Time of flight
2.883 s
Maximum height
10.194 m
Horizontal range
40.775 m
Time to reach max height
1.442 s
Recommended Settings
Pro Tips
- •A 45° launch angle maximizes horizontal range for a given launch speed, assuming no air resistance and equal launch and landing heights
- •Maximum height depends only on the vertical component of velocity (v₀sinθ), while range depends on both the vertical and horizontal components
- •The projectile reaches maximum height at exactly half its total time of flight, since the upward and downward halves of the motion are symmetric
- •Real-world trajectories are affected by air resistance, which this idealized model doesn't account for - actual range and height will be somewhat less than calculated here
Most Popular
Most physics problems test a 45° launch angle, since it produces the maximum range for a given speed
When to Use This Tool
Calculate time of flight, range, or maximum height for a classic projectile motion problem.
See how changing the launch angle trades off maximum height against horizontal range.
Get a rough estimate of a thrown or launched object's trajectory under ideal conditions.
Verify your own projectile motion calculation using the standard kinematic equations.
How It Works
Split the initial velocity into horizontal and vertical components using the launch angle
Calculate time of flight from the vertical component and gravitational acceleration, assuming launch and landing at the same height
Calculate maximum height and horizontal range using the standard projectile motion kinematic equations
100% Private
Files never leave your device. All processing happens locally in your browser.
Lightning Fast
Powered by Client-side kinematic calculation for optimal performance on modern browsers.
Open Source
Built with verified, open-source libraries. Fully transparent.
Frequently Asked Questions
Why is 45° the optimal angle for maximum range?
Range is proportional to sin(2θ), which reaches its maximum value of 1 when 2θ = 90°, meaning θ = 45° - any angle above or below 45° produces a shorter range for the same launch speed.
Does this account for air resistance?
No, this uses the standard idealized physics model that ignores air resistance. Real projectiles like balls or arrows will have somewhat shorter range and height due to drag.
What if my projectile launches and lands at different heights?
This calculator assumes launch and landing at the same height, which is the standard introductory physics scenario. A projectile launched from an elevated height would have a longer time of flight and range than this model calculates.
Is my data sent anywhere?
No. All calculations happen locally in your browser.