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- Calculates range, time of flight and maximum height of a launched object.
- Works from ground level or from a raised launch height.
- Supports metric and imperial units, plus custom gravity.
- Also gives impact speed and angle.
How to use the projectile motion calculator
Choose units
Metric (m, m/s) or imperial (ft, ft/s).
Enter speed and angle
The launch speed and the angle above horizontal.
Enter the launch height
0 for ground level, or the height of a cliff, table or roof.
Read the results
Range, flight time, peak height and impact speed appear at once.
Projectile motion equations
Velocity components
vₓ = v cos θ
vᵧ = v sin θ
Flight time, height and range
t = (vᵧ + √(vᵧ² + 2gh₀)) ÷ g
H = h₀ + vᵧ² ÷ 2g
R = vₓ × t
From ground level these simplify to t = 2vᵧ ÷ g and R = v² sin 2θ ÷ g.
Example 1: 20 m/s at 45°
From the ground, g = 9.81 m/s².
- Range 40.7747 m
- Flight time 2.8832 s
- Max height 10.1937 m
45° gives the longest range from ground level when air resistance is ignored.
Example 2: launched from a height
20 m/s at 30° from 10 m up.
- Range 48.0427 m
- Flight time 2.7737 s
- Max height 15.0968 m
From a height, the best angle for range is a little below 45°.
Example 3: other cases
More quick results.
- Thrown horizontally at 10 m/s from 20 m range 20.1928 m in 2.0193 s
- 100 ft/s at 45° (imperial) range 310.81 ft
Where a projectile motion calculator helps
Physics homework
Check kinematics answers and see the equations used.
Sports
Estimate how far a ball travels when kicked, thrown or hit.
Engineering and design
Get first estimates for launchers, sprinklers and fountains.
Games and animation
Make thrown objects move realistically.
The calculator ignores air resistance, spin and wind, so real objects usually fall short of these results. Find the angles of a launch triangle with the trig calculator, the peak of a quadratic path with the vertex form calculator, or solve for when it lands with the quadratic formula calculator.
Projectile motion calculator FAQ
What is projectile motion?
The curved path of an object launched into the air and moving under gravity alone.
What angle gives the maximum range?
45° from ground level, without air resistance. From a raised height, a slightly lower angle goes farther.
How do you calculate the range of a projectile?
From ground level, R = v² sin 2θ ÷ g. From a height, find the flight time first and multiply by the horizontal speed.
How do you find the maximum height?
H = v² sin²θ ÷ 2g, plus the launch height.
What value of g is used?
9.81 m/s² for metric and 32.174 ft/s² for imperial. You can enter your own, for example 1.62 m/s² for the Moon.
Does it include air resistance?
No. Air drag needs much more information and makes the path shorter and less symmetrical.