Calculate the maximum height reached by a projectile using its initial velocity, launch angle, and initial height. Enter your values and get the maximum height, time to reach peak, and vertical velocity component — all based on standard projectile motion physics.
Maximum Height
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Time to Reach Peak
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Vertical Velocity Component (V₀y)
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Horizontal Velocity Component (V₀x)
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The maximum height is reached when the vertical velocity component equals zero. Using the formula h = y₀ + (V₀·sin(α))² / (2g), where y₀ is the initial height, V₀ is the initial velocity, α is the launch angle, and g is gravitational acceleration, you can calculate the peak vertical position of any projectile.
The maximum height formula is: H = y₀ + (V₀y)² / (2g), where V₀y = V₀·sin(α). At maximum height, the vertical velocity component becomes zero, so the time to peak is t_h = V₀·sin(α) / g. Substituting back gives the full height equation.
For a ball thrown straight up (90° angle), the formula simplifies to H = y₀ + V₀² / (2g). Just enter 90° as the launch angle in the calculator and the vertical component equals the full initial velocity.
A launch angle of 90° (straight up) gives the maximum possible height for a given initial velocity, since all of the velocity is directed vertically. For maximum range (horizontal distance), 45° is optimal — but this trades off height for horizontal reach.
A 90° launch angle also results in the longest flight time for a given initial speed, because the projectile travels the greatest vertical distance before returning to its starting height. The time in the air is determined by vertical motion only.
No — in ideal projectile motion (ignoring air resistance), mass does not affect the maximum height. The only factors are the initial velocity, launch angle, initial height, and gravitational acceleration. This is consistent with Galileo's principle that all objects fall at the same rate regardless of mass.
The key factors are initial velocity, launch angle, initial height, and gravitational acceleration. In real-world scenarios, air resistance and wind also play a role, but these are not accounted for in standard projectile motion formulas. Gravity varies slightly by location and significantly on other celestial bodies.
Yes — the Initial Height (y₀) field lets you set a non-zero starting elevation. The calculator adds this to the height gained from the vertical velocity component, giving the total maximum height above the reference ground level.