Projectile Motion Calculator
Enter the launch speed, angle and starting height. You get the flight time, the range, the highest point and the landing speed.
Air resistance is ignored. A negative angle launches the object downwards.
Worked examples
Level ground
20 m/s at 45 degrees
Range 40.79 m, 2.88 s in the air, 10.2 m high
Range = v squared x sin(2 x angle) / g.
Dropped object
Launch speed 0 from a height of 20 m
2.02 s to land
sqrt(2 x 20 / 9.80665).
About Projectile Motion Calculator
Without air resistance, a thrown or launched object follows a curve called a parabola. The horizontal speed stays constant, while gravity changes the vertical speed at a steady rate. Splitting the launch speed into those two parts, using the sine and cosine of the launch angle, lets you work out how long the object is in the air, how far it travels and how high it climbs. This calculator does all of that and also gives the landing speed and angle.
On level ground the range is greatest at 45 degrees, and two angles that add up to 90 degrees, such as 30 and 60, give the same range. If you launch from a height, such as off a cliff or a table, the object stays in the air longer and the best angle is lower. Enter a starting height for that. Set the launch speed to zero to see how long an object takes to fall from rest. Change the gravity to see the same throw on the Moon or Mars.
How to use Projectile Motion Calculator
- Enter the launch speed, in metres per second or another unit.
- Enter the launch angle above the horizontal in degrees, with a negative angle for a downward throw.
- Enter the starting height above the landing level, and change gravity if you want another planet.
- Read the time in the air, range, greatest height, landing speed and landing angle.
Common uses
- Physics homework on projectiles and parabolas
- Working out how far a ball or javelin will travel
- Estimating the time for an object to fall from a height
- Comparing the same throw on the Moon and the Earth
Frequently asked questions
What angle gives the longest range?
On level ground, 45 degrees gives the longest range without air resistance. From a raised launch point the best angle is a little lower than 45 degrees.
Does the mass of the projectile matter?
Not without air resistance. A heavy and a light object launched with the same speed and angle follow the same path in a vacuum.
How is the time in the air found?
The vertical motion is solved for the time when the object returns to ground level. With a launch height h0, t = (vy + the square root of (vy squared + 2 g h0)) / g.
Why are real throws shorter?
Air resistance slows the object and removes energy, so real projectiles travel less far and land at a steeper angle than this idealised calculation.