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Calculation Machine

Projectile Motion Calculator

Range, height and flight time.

Reviewed by James Whitfield · How we check our maths

Your values

ⓘ Live results

Results
Range
62.7426 m
Maximum height
13.1618 m
Flight time
3.2762 s
Horizontal velocity
19.1511 m/s
Impact speed
25 m/s

Quick answer

Ignoring air resistance, a projectile's range is v²sin(2θ)/g, maximised at a 45° launch angle.

The formula

R = v² sin(2θ) / g

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Launch speed25 m/s
  • Launch angle40 degrees
  • Launch height0 m

Result

  • Range62.7426 m
  • Maximum height13.1618 m
  • Flight time3.2762 s
  • Horizontal velocity19.1511 m/s
  • Impact speed25 m/s

How to use the Projectile Motion Calculator

  1. 1Enter the launch speed in m/s.
  2. 2Enter the launch angle in degrees.
  3. 3Add a launch height if not from ground level.

Frequently asked questions

Why is 45° optimal?

It balances vertical hang time against horizontal speed — only true from level ground.

Does this include drag?

No, it assumes a vacuum; real ranges are shorter.

About this calculator