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Projectile Maximum Height

H=v02sin⁡2θ2gH = \frac{v_0^{2} \sin^{2}\theta}{2g}
sig figs

Worked example: 30 m/s straight up → 45.887 m. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter
gn=9.80665 m/s2g_{n} = 9.80665\ \text{m/s}^{2}Standard acceleration of gravity · exact

Where Projectile Maximum Height fits

In this toolkit

See also

Horizontal Velocity Component: Both use launch speed and launch angle.Projectile Range on Level Ground: Both use launch speed and launch angle.Projectile Time of Flight: Both use launch speed and launch angle.Vertical Velocity Component: Both use launch speed and launch angle.
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Projectile Maximum Height explained

θv0H

Only the vertical slice of the launch velocity, v₀ sin θ, fights gravity, and it is spent entirely by the time the projectile stops climbing, so the apex sits at v₀²sin²θ ⁄ 2g. Fire straight up at 30 m/s and you reach 30² ⁄ (2 × 9.80665) ≈ 45.9 m, about a 15-storey building. Galileo established the underlying parabola in Two New Sciences (1638) by rolling inked bronze balls off a table and marking where they struck: the first clean demonstration that horizontal and vertical motion proceed independently.

The common trap is squaring the sine rather than the whole term, or confusing this with the range formula's sin 2θ. Note how much steeper the sensitivity to angle is here than for range: a 60° launch reaches three times the height of a 30° launch at the same speed, yet lands at exactly the same spot. Basketball players exploit that trade: a high arc reaches the rim moving slowly and nearly straight down, which makes the hoop look bigger.

Projectile Maximum Height formula

H=v02sin⁡2θ2gH = \frac{v_0^{2} \sin^{2}\theta}{2g}
Where
  • HH= Maximum height (m)
  • v0v_0= Launch speed (m/s)
  • θ\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
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formula.expert. (2026, October 16). Projectile Maximum Height Formula & Calculator. https://formula.expert/solvers/projectile-maximum-height

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