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Maximum Height Of Projectile Calculator

Work out maximum height of projectile instantly with clear inputs, formula shown and shareable results.

About Maximum Height Of Projectile Calculator

Only the vertical component of the launch velocity fights gravity, so the peak height is (v sin theta)^2 divided by 2g. At the apex the vertical velocity is zero but the horizontal component is untouched, which is why the projectile is still moving there. Launching at 20 m/s and 60 degrees peaks at 15.3 m after 1.77 s.

Formulas

Maximum height

H = (v sin theta)^2 / (2g)

Time to apex

t = v sin theta / g

Worked example

With the default values below, Maximum Height Of Projectile Calculator returns Maximum Height of 15.296. Change any input above and every figure here is recalculated in your browser.

Inputs used

Launch speedminimum 0 m/s
20 m/s
Launch angle above horizontalaccepts 0–90 deg
60 deg
Gravitational accelerationminimum 0 m/s2
9.80665 m/s2

Results

Maximum Height
15.296 m
Time To Reach The Top
1.766 s
Initial Vertical Velocity
17.321 m/s
Speed At The Apex
10.000 m/s

Step by step

  1. 1Values used
  2. 2Maximum height
  3. 3Time to apex
  4. 4Maximum Height= 15.296 m
  5. 5Time To Reach The Top= 1.766 s
  6. 6Initial Vertical Velocity= 17.321 m/s
  7. 7Speed At The Apex= 10.000 m/s

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is the speed zero at the top?

No, only the vertical part is. The horizontal component v cos theta carries on unchanged, so the projectile is at its slowest but not stationary.

What launch angle gives the greatest height?

Straight up, 90 degrees. Height depends on sin theta while range depends on sin 2theta, which is why they peak at different angles.

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