HesapHanem

Projectile Max Height Calculator

Enter the launch velocity, angle, gravity, and initial height.

How it is calculated

Only the vertical part of the launch speed matters for the peak: vy = v × sin(θ). The rise above the launch point is rise = vy2 / (2g), the maximum height is h0 + rise, and the time to the top is vy / g. Units are metres, metres per second, degrees from the horizontal and m/s2 for gravity (9.81 on Earth, 1.62 on the Moon). Air resistance is ignored. The angle must be between 0 and 90 degrees, speed cannot be negative and gravity must be above zero; otherwise there is no result. Heights are rounded to two decimals.

Worked example

A ball leaves a 2 m high hand at 25 m/s and 40 degrees, with g = 9.81. Vertical speed: 25 × sin 40° = 25 × 0.6428 = 16.07 m/s. Rise: 16.072 / (2 × 9.81) = 258.2 / 19.62 = 13.16 m. Maximum height: 2 + 13.16 = 15.16 m. Time to apex: 16.07 / 9.81 = 1.64 s. The same throw at 90 degrees from the ground would rise 31.86 m.

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Common mistakes

  • Entering the angle in radians. The tool expects degrees, so 0.7 would be treated as under one degree.
  • Measuring the angle from the vertical. It is measured from the horizontal, and 90 degrees is straight up.
  • Expecting the height to be measured from the ground when h0 is left at 0. With h0 = 0 the result is the height above the launch point only.
  • Reading the rise and the maximum height as the same thing. They differ by the starting height.
  • Using the time to apex as the total flight time. It is only the way up; landing time needs the full trajectory, and the tool does not compute it.

Sources

About this calculator

For projectile motion under constant gravity, the maximum height above the launch point is reached when the vertical velocity component drops to zero, giving h = (v·sin θ)² ÷ (2g), where v is launch speed, θ is the launch angle from horizontal, and g is gravitational acceleration. Adding a nonzero starting height simply shifts the result: total peak height = initial height + (v·sin θ)² ÷ (2g).

This calculator takes launch velocity, angle, gravity, and initial height and returns the projectile's maximum height above the ground. Physics students use it to check kinematics homework on cannonballs, thrown balls, or launched rockets, and ballistics hobbyists and model rocketry enthusiasts use it to predict apogee for a given launch speed and angle before a real test.

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Comments (1)

  • Editorial team

    Here is a sanity check: at 45 degrees the peak is exactly half of what the same speed gives when thrown straight up, because sine squared of 45 degrees is one half. Remember the model is purely ballistic, with no air drag and no thrust after launch, so a motor-driven model rocket will not match it. What object and launch speed are you checking?

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