Projectile Motion Calculator
Calculate range, maximum height, time of flight, and velocity components for a projectile launched at any angle and speed. Assumes no air resistance.
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How to use this calculator
R = horizontal range; H = maximum height; T = total time of flight; v₀ = initial speed; θ = launch angle; g = 9.81 m/s².
- 1
Enter the initial speed and launch angle from horizontal.
- 2
Enter the launch height if the projectile starts above ground (default 0).
- 3
Gravity defaults to 9.81 m/s² (Earth). Change it to 1.62 for the Moon, 3.72 for Mars.
Frequently asked questions
What angle gives maximum range?
45° gives the maximum range on flat ground with no air resistance. For targets above the launch point, the optimal angle is less than 45°; for targets below, it is greater than 45°.
Does air resistance affect projectile motion?
Yes, significantly at high speeds. This calculator assumes vacuum conditions (no air resistance), which gives accurate results for slow projectiles over short distances but overestimates range for bullets, baseballs, and similar high-speed objects.
How do I use this for different planets?
Change the gravity value: Moon = 1.62 m/s², Mars = 3.72 m/s², Jupiter = 24.79 m/s². Range increases dramatically on low-gravity bodies.
Projectile Motion Calculator — Range, Height & Time of Flight
How projectile motion works
Projectile motion decomposes into two independent components: constant horizontal velocity (vₓ = v₀cosθ) and uniformly accelerated vertical motion (vy = v₀sinθ − gt). Because they are independent, the horizontal distance depends on both the speed and how long the projectile stays airborne.
Maximum range vs maximum height
There is a direct trade-off between range and height. Launching at 45° maximises range but the peak height is moderate. Launching at 75° gives a much higher peak but a shorter range. Launching at 15° gives the same range as 75° (complementary angles) but with a very flat, low trajectory.
Projectile motion: how it works
Built on well-established mathematical principles, this tool delivers accurate results for students, researchers, and professionals. Enter your values and get instant clarity without specialist software or manual arithmetic.
Who uses this tool?
Teachers, students, engineers, and data analysts use it to verify calculations, check homework, and solve problems faster. It is intuitive enough for beginners while comprehensive enough for professional use.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →