Projectile Maximum Height Calculator
Enter initial speed and launch angle to compute the maximum height H = (v₀²·sin²θ)/(2·g) of a projectile.
Input Data
Results
At a glance:The maximum height of a projectile (no air resistance) occurs when the vertical velocity reaches zero. Using v_y = v₀·sinθ and kinematics v_y² = 2gH, H = (v₀²·sin²θ)/(2g). The vertical component of initial speed sets the height; the horizontal component does not affect it. At θ=90° (straight up) H = v₀²/(2g); at θ=0° H=0. This result assumes constant g and negligible drag; with air resistance the real height is lower. This tool returns H from v₀, θ and g.
Formula
H = (v₀²·sin²θ)/(2g)
$$H = \frac{(v_0 \sin\theta)^2}{2g}$$How to Use
- Enter initial speed v₀ (m/s).
- Enter launch angle θ (°) and gravity g.
- The calculator returns the max height H.
Case Studies
Football punt
v₀ = 25 m/s, θ = 60°, g = 9.81.
H = 625×0.75/(2×9.81) ≈ 23.9 m.
High, hanging punt.
FAQ
Why only the vertical component matters?
Height depends on the initial upward speed v₀·sinθ; the horizontal speed v₀·cosθ affects range, not how high it goes.
What angle gives max height for a fixed speed?
θ=90° (straight up), giving H = v₀²/(2g). Any lower angle reduces the vertical component and thus the height.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.