Practical tools for measured work
Projectile and free fall calculator
Calculate ideal flight time, range, height and impact speed with a trajectory diagram.
Calculate the layout, check the diagram, then print the result for the shop or jobsite.
Trajectory samples
| Time (s) | Horizontal distance (m) | Height (m) | Vertical velocity (m/s) |
|---|---|---|---|
| 0 | 0 | 0 | 7.071067812 |
| 0.2403494164 | 1.699527022 | 1.416272518 | 4.714045208 |
| 0.4806988327 | 3.399054043 | 2.266036029 | 2.357022604 |
| 0.7210482491 | 5.098581065 | 2.549290532 | -8.881784197e-16 |
| 0.9613976654 | 6.798108087 | 2.266036029 | -2.357022604 |
| 1.201747082 | 8.497635108 | 1.416272518 | -4.714045208 |
| 1.442096498 | 10.19716213 | 0 | -7.071067812 |
How it works
Horizontal position x = v₀ cos(θ)t. Height y = h₀ + v₀ sin(θ)t − gt²/2. Flight ends at the nonnegative ground intersection. To model an object dropped from rest, enter zero launch speed and a positive height.
At g = 10 m/s², dropping from 20 m takes 2 s and reaches 20 m/s. A 10 m/s launch at 45° from ground level travels 10 m and reaches 2.5 m. The diagram uses equal horizontal and vertical scales.
Current-input example
The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.
- Launch speed
- 10 m/s
- Launch angle above horizontal
- 45 °
- Launch height above ground
- 0 m
- Gravitational acceleration
- 9.80665 m/s²
Primary result: Flight time: 1.442096498 s.
Before using the result
- Check the selected mode, units and input values before using the result.
- Read the assumptions and rounding rules; compare the worked example with your intended calculation.
- A numerical result does not supply missing context or change the stated limitations.
Limitations
Flat ground, constant positive gravity and no air resistance. Height and launch speed must be nonnegative; angle must lie between −90° and 90°. Terrain, wind, terminal velocity and Earth curvature are excluded. An object launched downward from ground level has zero flight time.
Frequently asked questions
What is the difference between speed and velocity?
Average speed is total path length divided by elapsed time. Average velocity is signed displacement divided by elapsed time. Returning to the starting point gives zero average velocity even after travelling a nonzero distance.
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