# Sled Ride Calculator

URL: https://speedycalculator.com/calculators/physics/sled/
Last updated: 2026-10-30

> The sled ride calculator finds the acceleration, top speed at the bottom and ride time for a sled sliding down a snowy hill, from the type of sled (friction), the hill angle and its length or height.

## Inputs

- Type of sled
- Hill angle (°, rad, arcmin, arcsec, mrad)
- I know the hill…
- Hill length (m, cm, mm, km, in, ft, yd, mi)
- Hill height (m, cm, mm, km, in, ft, yd, mi)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Acceleration
- Speed at the bottom
- Ride time
- Hill length

## Formula

```
a = g(sin θ − μ cos θ),  v = √(2aL),  t = √(2L/a)
```

## Explanation

Sledding is an inclined plane experiment you can do every winter. The steeper the hill and the slicker the runners, the faster you go – but friction and air drag keep real speeds below these ideal values.

### How to use the Sled Ride Calculator

- **Type of sled**
- **Hill angle**
- **I know the hill…**
- **Hill length**
- **Hill height**
- **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

Choose your sled (each has a typical friction coefficient on snow), the hill angle and either its length along the slope or its height.

### Inputs explained

FieldWhat to enterType of sledChoose one: Steel runners on ice, Plastic sled on packed snow, Inflatable snow tube, Wooden toboggan on snow …Hill angleUnits: °, rad, arcmin, arcsec, mradI know the hill…Choose one: Length (along the slope), HeightHill lengthUnits: m, cm, mm, km, in, ft …Hill heightUnits: m, cm, mm, km, in, ft …Gravitational acceleration gUnits: m/s², ft/s², g, cm/s²

### What each result means

- **Acceleration** = max(0, [Gravitational acceleration g]×(sin(rad([Hill angle])) - [Type of sled]×cos(rad([Hill angle]))))
- **Speed at the bottom** = sqrt(2×[Acceleration]×[L])
- **Hill length** = [L]

### Example values

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

Hill angle (°)Speed at the bottom (km/h)7.532.0811.2543.081551.7318.7559.0222.565.43076.19

## Worked example

Inputs — Type of sled: Plastic sled on packed snow; Hill angle: 15 °; I know the hill…: Length (along the slope); Hill length: 50 m; Gravitational acceleration g: 9.80665 m/s².

Results — Acceleration = 2.0645 m/s²; **Speed at the bottom = 51.73 km/h**; Ride time = 6.96 s; Hill length = 50 m.

## Key terms

- **Kinetic friction**: Friction between surfaces sliding past each other.

## FAQ

**Why do I go faster on ice?**
The friction coefficient of runners on ice is very low.

**Does a heavier rider go faster?**
Without air drag, no; with drag, heavier riders reach slightly higher speeds.

**What is a safe sledding slope?**
Gentle slopes (under about 15°) with a long flat run-out.

**Why is my real speed lower?**
Air resistance and uneven snow slow you down.


## 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)