# Projectile Motion Experiment Calculator

URL: https://speedycalculator.com/calculators/physics/projectile-motion-experiment/
Last updated: 2026-10-30

> The projectile motion experiment calculator predicts where a ball launched at a given speed, angle and height will land, its time of flight and maximum height, and its position and velocity at any moment.

## Inputs

- Launch speed v₀ (m/s, km/h, mph, ft/s, knots, km/s)
- Launch angle α (°, rad, arcmin, arcsec, mrad)
- Launch height h (m, cm, mm, km, in, ft, yd, mi)
- Time of interest t (s, ms, min, h, days)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Time of flight
- Horizontal distance (range)
- Maximum height
- Horizontal position at t
- Height at t
- Speed at t

## Formula

```
x = v₀cosα·t,  y = h + v₀sinα·t − ½gt²,  range from y = 0
```

## Explanation

Throwing a ball, kicking a football or launching a water rocket all follow parabolic paths. This calculator lets you plan and check a classroom experiment, including the position at a chosen time.

### How to use the Projectile Motion Experiment Calculator

- **Launch speed v₀**
- **Launch angle α**
- **Launch height h**
- **Time of interest t**
- **Gravitational acceleration g**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the launch speed, angle and height, and a time at which to see the position.

### Inputs explained

FieldWhat to enterLaunch speed v₀Units: m/s, km/h, mph, ft/s, knots, km/sLaunch angle αUnits: °, rad, arcmin, arcsec, mradLaunch height hUnits: m, cm, mm, km, in, ft …Time of interest tUnits: s, ms, min, h, daysGravitational acceleration gUnits: m/s², ft/s², g, cm/s²

### What each result means

- **Time of flight** = ([vy] + sqrt([vy]^2 + 2×[Gravitational acceleration g]×[Launch height h]))÷[Gravitational acceleration g]
- **Horizontal distance (range)** = [vx]×([vy] + sqrt([vy]^2 + 2×[Gravitational acceleration g]×[Launch height h]))÷[Gravitational acceleration g]
- **Maximum height** = [Launch height h] + max(0, [vy])^2÷(2×[Gravitational acceleration g])
- **Horizontal position at t** = [vx]×[Time of interest t]
- **Height at t** = [Launch height h] + [vy]×[Time of interest t] - [Gravitational acceleration g]×[Time of interest t]^2÷2
- **Speed at t** = sqrt([vx]^2 + ([vy] - [Gravitational acceleration g]×[Time of interest t])^2)

### Example values

How the main result changes when **Launch speed v₀** changes and everything else stays at the example values above:

Launch speed v₀ (m/s)Horizontal distance (range) (m)42.403564.5687.45451011.11861215.56781626.8492

## Worked example

Inputs — Launch speed v₀: 8 m/s; Launch angle α: 40 °; Launch height h: 1 m; Time of interest t: 0.5 s; Gravitational acceleration g: 9.80665 m/s².

Results — Time of flight = 1.2164 s; **Horizontal distance (range) = 7.45453 m**; Maximum height = 2.34823 m; Horizontal position at t = 3.06418 m; Height at t = 2.34532 m; Speed at t = 6.13301 m/s.

## Key terms

- **Projectile**: Object moving only under gravity after launch.

## FAQ

**What angle gives the longest range?**
45° from ground level; less when launched from a height.

**Does air resistance matter?**
Yes for light or fast objects – this calculator ignores it.

**Why is the path a parabola?**
Horizontal speed is constant while gravity accelerates the ball downwards.

**What if the height at t is negative?**
The ball has already landed.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)