BALLISTICS & TRAJECTORY
Projectile Motion Calculator
Range, max height, and time of flight for arcing projectiles — with trajectory preview.
PROJECTILE PHYSICS
Calculate the arc
Projectile motion guide
Arcing projectiles — grenades, fireballs, arrows — all follow the same physics: a straight-line launch velocity bent by gravity into a parabola. This calculator gives you range, max height, time of flight, and a live trajectory preview for any launch speed, angle, and gravity.
The three numbers of an arc
Range = v²·sin(2θ) ÷ g. Max height = v²·sin²(θ) ÷ 2g. Time of flight = 2·v·sin(θ) ÷ g. All three fall out of the launch velocity and angle — nothing else matters in a vacuum.
The famous consequence: 45° gives maximum range. Every other angle has a twin that lands at the same distance (e.g. 30° and 60°), so players can lob over cover at either a flat or a steep angle.
Aiming with fixed angles
Most games fire at a fixed angle (like 45°) and compute the velocity needed to reach a target: v = √(range·g ÷ sin(2θ)). That is how mortar-style weapons and grenade arcs stay consistent regardless of distance.
Tip: For gameplay, gravity in units/s² should match your world scale — 9.81 feels right in meter-scale Unity scenes; 20–40 is snappier for stylized games. Tune the arc to readability, not realism.
Frequently asked questions
What angle gives the longest range?
45° — with the same launch speed, no other angle travels further. Use it as the default for lobbed projectiles.
How do I make a projectile hit a specific target?
Fix your launch angle and solve for speed: v = √(range·g / sin(2θ)). Or fix speed and solve for angle: θ = ½·arcsin(range·g / v²).
Why does my grenade arc look wrong?
Check your gravity units. If your world uses units ≈ meters, 9.81 gives real-feeling arcs. If it feels floaty or slingshot-y, your gravity is too low or too high for the launch speed.
Privacy note: projectile calculations happen in your browser. Nothing is uploaded.