Projectile Range Calculator
Work out projectile range instantly with clear inputs, formula shown and shareable results.
About Projectile Range Calculator
For launch and landing at the same height, the range is v^2 sin(2theta)/g. The sine of twice the angle peaks at 45 degrees, which is why that angle throws furthest, and why 30 and 60 degrees give identical ranges. At 20 m/s and 45 degrees the range is about 40.8 m with a 2.9 s flight.
Formulas
Range
R = v^2 x sin(2theta) / g
Time of flight
t = 2v sin(theta) / g
Worked example
With the default values below, Projectile Range Calculator returns Horizontal Range of 40.789. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Launch speedminimum 0 m/s
- 20 m/s
- Launch angle above horizontalaccepts 0–90 deg
- 45 deg
- Gravitational accelerationminimum 0 m/s2
- 9.80665 m/s2
Results
- Horizontal Range
- 40.789 m
- Time Of Flight
- 2.884 s
- Horizontal Velocity Component
- 14.142 m/s
- Maximum Possible Range At 45 Degrees
- 40.789 m
Step by step
- 1Values used
- 2Range
- 3Time of flight
- 4Horizontal Range= 40.789 m
- 5Time Of Flight= 2.884 s
- 6Horizontal Velocity Component= 14.142 m/s
- 7Maximum Possible Range At 45 Degrees= 40.789 m
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why do 30 and 60 degrees give the same range?
Because sin(60) and sin(120) are equal. The steeper launch stays up longer but moves horizontally more slowly, and the two effects cancel exactly.
Does air resistance change the best angle?
Yes. With drag the optimum drops to roughly 35-40 degrees, and lower still for light objects such as a shuttlecock.