Projectile Time of Flight

Also known as hang time

T = \frac{2 v_0 \sin\theta}{g}

sig figs

Worked example: 25 m/s at 30° → 2.549 s. Press Try an example to run it live, then adjust anything.

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Constant used: built into this formula, no need to enter

g_{n} = 9.80665\ \text{m/s}^{2}

Standard acceleration of gravity · exact

Where Projectile Time of Flight fits

In this toolkit

The projectile motion equations6 formulas

The height of a throw →

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Projectile Time of Flight explained

Hang time depends only on the vertical launch velocity: the projectile takes v₀ sin θ ⁄ g to reach the top and exactly as long to fall back, giving T = 2v₀ sin θ ⁄ g. Launch at 25 m/s and 30° and the vertical component is 12.5 m/s, so the flight lasts 2 × 12.5 ⁄ 9.80665 ≈ 2.55 s. Nothing about the horizontal speed appears, which is Galileo's independence principle in its most testable form, the same insight behind his claim that a stone dropped from a moving ship's mast lands at the mast's foot.

Two cautions. First, this assumes the landing height equals the launch height; throw off a cliff or off a 2 m-tall shoulder and the real flight is longer, requiring the full quadratic. Second, the formula is symmetric, so a given time of flight matches two speeds only through the angle: solving for θ returns the principal arcsin branch (0° to 90°), and the supplementary angle 180° − θ gives the identical hang time on a lower, faster trajectory.

Projectile Time of Flight formula

T = \frac{2 v_0 \sin\theta}{g}

Where

$T$ = Time of flight (s)
$v_0$ = Launch speed (m/s)
$\theta$ = Launch angle (°)

In this toolkit

The projectile motion equations

6 formulasRange, maximum height, time of flight and the two velocity components — the standard results for a projectile launched into still air.

Revised 16 October 2026

Cite this page

formula.expert. (2026, October 16). Projectile Time of Flight Formula & Calculator. https://formula.expert/solvers/projectile-time-of-flight

https://formula.expert/solvers/projectile-time-of-flight