Free · Physics models
Ideal Projectile Flight Time to Ground
Find the landing time for a projectile launched at a known speed, angle and height above ground.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- 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
velocityHorizontal = 17.321; velocityVertical = 10.000. This worked example uses the displayed units and declared assumptions.
velocityHorizontal = velocity * cos(angle); velocityVertical = velocity * sin(angle); timeFlight = (velocityVertical + (velocityVertical^2 + 2 * 9.80665 * initialHeight)^(1/2))/9.80665; velocity^2 = velocityHorizontal^2 + velocityVertical^2
Worked example
Enter these known values and leave the other values blank.
- Velocity
- 20 m/s
- Angle of launch
- 30 deg
- Initial height
- 10 m
- Time of flight
- 2.774 sec
- Horizontal velocity
- 17.32 m/s
- Vertical velocity
- 10 m/s
Assumptions and limitations
- A point projectile moves in a vertical plane with constant downward acceleration 9.80665 m/s². Launch angle is measured above the horizontal, and initial height is nonnegative above flat ground. Air resistance and Earth curvature are omitted.
- Flight time is the nonnegative root of y(t)=h+vy*t−g*t²/2. The native right triangle illustrates horizontal and vertical launch-velocity components, with speed as the hypotenuse.
Common questions
What assumptions apply?
A point projectile moves in a vertical plane with constant downward acceleration 9.80665 m/s². Launch angle is measured above the horizontal, and initial height is nonnegative above flat ground. Air resistance and Earth curvature are omitted.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
A point projectile moves in a vertical plane with constant downward acceleration 9.80665 m/s². Launch angle is measured above the horizontal, and initial height is nonnegative above flat ground. Air resistance and Earth curvature are omitted. Flight time is the nonnegative root of y(t)=h+vy*t−g*t²/2. The native right triangle illustrates horizontal and vertical launch-velocity components, with speed as the hypotenuse.