The time a projectile spends in the air depends only on its vertical motion: the vertical launch speed and the height it starts from. A ball thrown horizontally from a table and one dropped from the same height land at the same time.
How to use the Time of Flight Calculator – Projectile Motion
- Initial velocity v₀
- Angle of launch α
- Initial height h₀
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
The vertical position h₀ + v_y·t − ½gt² is set to zero and solved for t.
Inputs explained
| Field | What to enter |
|---|---|
| Initial velocity v₀ | Units: m/s, km/h, mph, ft/s, knots, km/s |
| Angle of launch α | Units: °, rad, arcmin, arcsec, mrad |
| Initial height h₀ | Units: m, cm, mm, km, in, ft … |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Horizontal velocity vₓ = [vx]
- Initial vertical velocity v_y = [vy]
- Time of flight = [time of flight]
- Range (horizontal distance) = [vx]×[time of flight]
- Impact speed = sqrt([vx]^2 + ([vy] – [Gravitational acceleration g]×[time of flight])^2)
- Impact angle (below horizontal) = deg(atan2([Gravitational acceleration g]×[time of flight] – [vy], [vx]))
Example values
How the main result changes when Initial velocity v₀ changes and everything else stays at the example values above:
| Initial velocity v₀ (m/s) | Time of flight (s) |
|---|---|
| 7.5 | 0.7648 |
| 11.25 | 1.1472 |
| 15 | 1.5296 |
| 18.75 | 1.912 |
| 22.5 | 2.2944 |
| 30 | 3.0591 |
Formula
t = (v·sin α + √((v·sin α)² + 2gh₀)) / g; from the ground: t = 2v·sin α / g
Worked example
Inputs — Initial velocity v₀: 15 m/s; Angle of launch α: 30 °; Initial height h₀: 0 m; Gravitational acceleration g: 9.80665 m/s².
Results — Horizontal velocity vₓ = 12.990381 m/s; Initial vertical velocity v_y = 7.5 m/s; Time of flight = 1.529574 s; Range (horizontal distance) = 19.869753 m; Maximum height = 2.867952 m; Time to maximum height = 0.764787 s; Impact speed = 15 m/s; Impact angle (below horizontal) = 30 °.
Key terms
- Time of flight
- Duration from launch to landing.
Frequently asked questions
What angle gives the longest range?
45° on flat ground without air resistance; lower angles win when launching from a height.
Does mass affect a projectile without air resistance?
No – all objects fall with the same acceleration g.
Why are the horizontal and vertical motions independent?
Gravity acts only vertically, so the horizontal velocity stays constant.
How accurate is this for real balls?
Air resistance shortens the range, especially for light or fast objects.