Time of Flight Calculator – Projectile Motion

Time of flight for projectile motion

Check out how long a projectile remains in the air with this time of flight calculator.

Last updated: December 26, 2025

CreatorFrank Zhao

Time of Flight Projectile Motion Diagram

Inputs

Velocity

More info

m/s

Angle of launch

More info

deg

Initial height

More info

Results

Time of flight

More info

sec

Horizontal velocity

More info

m/s

Vertical velocity

More info

m/s

1Calculate Horizontal Velocity

v_x = v\cos(\alpha)

2Calculate Vertical Velocity

v_y = v\sin(\alpha)

3Calculate Time of Flight

t = \frac{v_y + \sqrt{v_y^2 + 2gh}}{g}

4Pythagorean Theorem for Velocity

v^2 = v_x^2 + v_y^2

v

Velocity

v_x

Horizontal velocity

v_y

Vertical velocity

\alpha

Angle of launch

h

Initial height

g

Gravity

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Time of flight equation

In ideal projectile motion, the vertical position changes due to gravity. A convenient starting point is the vertical motion equation.

y = v_0\,t\,\sin(\alpha) - \frac{1}{2} g\,t^2

Here $v_0$ , $t$ , $\alpha$ , and $g$ represent the initial speed, time, launch angle, and gravitational acceleration.

Two common cases

Launching from the ground (starting height $h = 0$ ): the time of flight simplifies to a short expression.
Launching from an elevated point (starting height $h > 0$ ): the square-root term appears because the projectile has “extra distance” to fall.

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Nice combo:

If you also care about how far the projectile travels, try our Projectile Range Calculator.

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How to use / quick start guide

Enter the initial speed

Type your launch speed and choose the unit you want to work in.

Set the launch angle

Use degrees or radians. A larger angle increases the vertical component $v_y = v\sin(\alpha)$ .

Add a starting height (optional)

If you start above ground level, enter $h$ . Otherwise leave it at $0$ .

Read the time of flight

The calculator shows the total flight time $t$ . You can also open “Velocity components” to see $v_x$ and $v_y$ .

Diagram (the same one shown above the calculator)

Projectile motion diagram used in the calculator

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Time of flight exemplary calculations

Example A: launch from ground

Suppose you throw a ball with $v_0 = 20\,\mathrm{m/s}$ at $\alpha = 35^\circ$ from ground level ( $h = 0$ ).

t

=

\frac{2\,v_0\,\sin(\alpha)}{g}

=

\frac{2\cdot 20\cdot \sin(35^\circ)}{9.80665}

\approx

2.34\,\mathrm{s}

Interpretation: the projectile stays in the air for about $2.34\,\mathrm{s}$ .

Example B: launch from an elevated point

A small pebble is tossed at $v_0 = 16\,\mathrm{ft/s}$ and $\alpha = 20^\circ$ from a height $h = 6000\,\mathrm{ft}$ .

t

=

\frac{v_0\sin(\alpha)+\sqrt{(v_0\sin(\alpha))^2+2gh}}{g}

t

\approx

\frac{16\sin(20^\circ)+\sqrt{(16\sin(20^\circ))^2+2\cdot 32.174\cdot 6000}}{32.174}

\approx

19.5\,\mathrm{s}

Reminder: these examples assume “ideal” motion (no air resistance). Real trajectories usually fall a bit sooner and travel a bit less.

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Real-world examples / use cases

Sports training

Estimate hang time for a thrown ball to plan timing (passes, catches, or trick shots).

Archery basics

Compare high-angle vs low-angle shots by looking at how the vertical component changes.

Classroom physics

Quickly generate a consistent set of values for homework checks or lab worksheets.

Drone payload drops (simplified)

Roughly estimate how long an object is in free fall from a known height (ignoring drag).

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Tip:

If you want to focus on purely horizontal launches, check the Horizontal Projectile Motion Calculator.

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FAQs

How can I calculate time of flight?

For a ground launch ( $h = 0$ ) in ideal motion, a common form is $t = \frac{2\,v_0\sin(\alpha)}{g}$ .

What is the time of flight equation for an elevated launch?

When $h > 0$ , you’ll often see the formula expressed in a compact form. To keep it readable on small screens, here it is split into two lines using a helper term.

t

=

\frac{v_0\sin(\alpha)+\sqrt{\Delta}}{g}

\Delta

=

(v_0\sin(\alpha))^2 + 2gh

Which launch angle gives the longest time in the air?

In the ideal model with fixed $v_0$ and $h$ , increasing $\alpha$ increases the vertical component $v_0\sin(\alpha)$ . The maximum occurs at $\alpha = 90^\circ$ (straight up).

What does “time of flight” mean in physics?

It’s the total duration from launch until the object reaches the ground again — in other words, the full interval $t$ measured from the start of motion.

Is air resistance included?

No. This calculator follows the standard “ideal projectile” assumption. If drag is important (fast objects, long distances), real results can differ.

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Limitations / disclaimers

This calculator is for educational and planning purposes. It does not replace professional engineering analysis. Results assume uniform gravity and no air resistance.

If you’re working with high-speed projectiles, drag can materially change flight time.
For extremely long ranges, $g$ may vary slightly with location and altitude.
Always double-check units (especially when mixing metric and imperial inputs).

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