Time of Flight Calculator – Projectile Motion

How to use this time of flight calculator

What this calculator does

This calculator estimates the duration and ideal path of a projectile launched above a horizontal landing level. It treats horizontal and vertical motion separately, assumes constant Earth gravity of 9.80665 m/s², and neglects aerodynamic drag, wind, lift, spin, changing gravity, and terrain curvature. The primary result is Time of flight, meaning the elapsed time from launch until the projectile reaches the landing level. The related outputs help you inspect how that answer is produced, but they are still model estimates rather than a prediction of a real object in turbulent air.

When to use it

Use the calculator to check introductory mechanics exercises, estimate the ideal airtime of a ball or launched object, compare launch angles while holding speed and height constant, or build a first-pass engineering model before adding drag. The underlying separation of horizontal and vertical motion is explained in the OpenStax projectile-motion chapter.

How to calculate

1. The calculator opens with a complete demonstration: Velocity 16 ft/s, Angle of launch 20°, and Initial height 6,000 ft. Its results and a validated example workbook are available immediately.
2. Replace the demonstration values with your own. Select the matching Velocity unit and Initial height unit; changing either unit converts the value already entered rather than merely relabeling it.
3. Read Time of flight first, then review the velocity components, range, peak height, trajectory line, and sample table. Results update as you type.
4. Select Download Excel to create a current-state workbook containing inputs, outputs, assumptions, and all trajectory rows. Select Reset to clear the demonstration and computed state. Reset may disable Excel export until all required inputs are complete and valid again.

Input guide

Velocity is a required nonnegative decimal launch speed. It accepts m/s, km/h, ft/s, or mph and uses a decimal point; 16 ft/s is the demonstration value. Higher velocity generally increases airtime when the launch has an upward component, and it increases horizontal travel. Do not paste scientific notation or decimal-comma text such as “1,5”; the calculator rejects ambiguous formats instead of silently changing their meaning. Velocity unit is required and controls both input conversion and the velocity outputs.

Angle of launch is a required decimal from 0° through 90°, measured above the horizontal. The demonstration uses 20°. Increasing the angle raises the initial vertical velocity and usually lengthens airtime, while reducing the horizontal component. A common mistake is entering radians; this field always uses degrees. At 0°, the launch is horizontal. At 90°, horizontal range is zero, so the trajectory chart is replaced by a compact non-chart summary state.

Initial height is the required vertical distance from the launch point to the landing level, expressed in meters or feet. It must be zero or positive; 6,000 ft is the demonstration value. A larger height gives the projectile farther to fall and therefore increases flight time. Initial height unit is required and converts the current value between meters and feet. Do not enter elevation above sea level unless the landing level is sea level; the input is a relative height difference.

Output guide

Time of flight is the total duration in seconds and is the calculator's primary estimate. Horizontal range is the ideal horizontal distance to impact in the selected height unit. Peak height is the maximum height above the landing level, not merely the rise above launch. Time to apex is when the initial upward vertical velocity reaches zero; it is zero for a horizontal launch.

Horizontal velocity is constant in this no-drag model. Initial vertical velocity is the upward component at launch. Impact vertical velocity is normally negative because downward is represented by a negative sign. Impact speed is the nonnegative magnitude formed from the horizontal and vertical impact components. The Trajectory profile plots height against horizontal distance, and the Trajectory samples table lists Sample, Time, Distance, Height, Horizontal velocity, and Vertical velocity from launch through impact. Zero horizontal range is valid for a vertical launch, but a line chart would not provide a meaningful horizontal comparison, so no chart is drawn in that state.

Worked example

For the opening values, 16 ft/s converts to 4.8768 m/s and 6,000 ft converts to 1,828.8 m. The 20° launch gives an initial vertical component of about 1.667964 m/s. The calculator solves the positive root of the vertical-position equation:

Using g = 9.80665 m/s² produces 19.483 seconds, matching the first-open result. Multiplying that time by the horizontal component produces an ideal range of about 292.93 ft. The workbook uses the same unrounded canonical values as the page and table.