# Projectile Motion Calculator

URL: https://speedycalculator.com/calculators/physics/projectile-motion/
Last updated: 2026-10-25

> The projectile motion calculator finds the range, maximum height and flight time of a projectile launched from ground level at a given speed and angle, ignoring air resistance.

## Inputs

- Launch speed (m/s, km/h, mph, ft/s, knots)
- Launch angle (°)
- Gravitational acceleration (m/s², ft/s², g)

## Results

- Horizontal range
- Maximum height
- Time of flight

## Formula

```
Range = v² sin(2θ) ÷ g
Max height = v² sin²θ ÷ 2g
Time = 2v sin θ ÷ g
```

## Explanation

A projectile follows a parabola. On level ground, 45° gives the longest range without air resistance.

### How to use the Projectile Motion Calculator

- **Launch speed**
- **Launch angle**
- **Gravitational acceleration**
- Want to work backwards? Type a value into **Horizontal range** and **Launch speed** is calculated for you.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The launch velocity is split into horizontal and vertical components, and the equations of motion are applied to each.

### Inputs explained

FieldWhat to enterLaunch speedUnits: m/s, km/h, mph, ft/s, knotsLaunch angleIn °Gravitational accelerationUnits: m/s², ft/s², g

### What each result means

- **Horizontal range** = [Launch speed]^2 × sin(rad(2×[Launch angle])) ÷ [Gravitational acceleration]
- **Maximum height** = [Launch speed]^2 × sin(rad([Launch angle]))^2 ÷ (2×[Gravitational acceleration])
- **Time of flight** = 2×[Launch speed]×sin(rad([Launch angle])) ÷ [Gravitational acceleration]

### Example values

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

Launch speed (m/s)Horizontal range (m)1010.21522.942040.792563.733091.7740163.15

## Worked example

Inputs — Launch speed: 20 m/s; Launch angle: 45 °; Gravitational acceleration: 9.80665 m/s².

Results — **Horizontal range = 40.79 m**; Maximum height = 10.2 m; Time of flight = 2.884 s.

## FAQ

**Why is 45° best?**
sin(2θ) is largest at 90°, so θ = 45° on level ground.

**What about launching from a height?**
The range increases and the best angle is below 45°.

**What formula does the Projectile Motion Calculator use?**
Range = v² sin(2θ) ÷ g.

**Can I work backwards from the result?**
Yes. Type the result you want into Horizontal range and the calculator finds the matching launch speed.


## Sources

- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)