Free · Kinematics calculators — How things move ⏱️

Projectile Apex Height and Velocity Components

Calculate projectile apex height and velocity components with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

velocity x = 8.660254; velocity y = 5; height max = 3.2746453. Values use the worked example unit selections.

hmax = h0 + (v sinθ)²/(2g); vx = v cosθ; vy = v sinθ

Worked example

Enter these known values and leave the other values blank.

Velocity
10 m/s
Angle of launch
30 deg
Initial height
2 m
Horizontal velocity
8.66 m/s
Vertical velocity
5 m/s
Maximum height
3.275 m

Assumptions and limitations

  • Constant standard gravity 9.80665 m/s² and no air resistance are assumed. The launch is upward with a principal angle from zero to 90 degrees. Height is relative to the same datum as the initial position.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.

Common questions

What does this calculation assume?

Constant standard gravity 9.80665 m/s² and no air resistance are assumed. The launch is upward with a principal angle from zero to 90 degrees. Height is relative to the same datum as the initial position.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Original accessible explanations preserve the captured diagram geometry, quantities and conditional variants without external image loading. Restrict the physical model to non-singular dimensions and stated principal inverse branches; discrete gear/fringe counts are exact integers. The captured floor(angle/90) height inverse cannot recover launch speed from apex height because its radian angle domain always makes that divisor zero. Constant-gravity energy yields hmax=h0+vy²/(2g), with positive upward root vy=sqrt(2gΔh) and v=vy/sinθ. Keep all four targets and the same equation count; remove only the false dependency/singularity.

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