# Gear Ratio Speed Calculator

Table of contents

How do I use the gear ratio speed calculator?How to calculate the gear ratio for gear speed?The relationship between the gear ratio and the speed ratioRelated calculatorsFAQsWelcome to the **gear ratio speed calculator**! Here, we'll show you:

**How to calculate the gear ratio**and the**speed at which your output gear rotates**relative to your input gear; and**How to calculate speed from the gear ratio**.

*Ready to roll?*

## How do I use the gear ratio speed calculator?

The **gear ratio speed calculator** is easy to use and understand. Follow these simple steps:

**Enter the number of teeth**in each of your two gears. Make sure you know which is the driving gear and which one is driven!- Alternatively,
**to obtain the number of teeth for either gear for a suitable speed ratio**, enter one gear's number of teeth and a suitable gear ratio instead. - Under the field for the gear ratio, we explain
**how the gear ratio influences the speed ratio**between the input and output gears. - You can also
**enter an input speed**to find the output speed corresponding to the two-gear system you've created above.

And that's it! You now know how to use the **gear ratio speed calculator**!

## How to calculate the gear ratio for gear speed?

When you have two connected gears, the **gear ratio** is the ratio between the **input (driving) gear's number of teeth** and the **output (driven) gear's number of teeth**. It allows the system designer to slow or speed up a rotational speed, which has other useful effects like influencing the torque. The gear ratio is also the factor by which the input speed is multiplied to deliver the output speed.

So, if you want to know **how to calculate the gear ratio** and the **speed ratio** mathematically, the equation would be:

For example, a two-gear system featuring an input gear with $10$ teeth and an output gear with $20$ teeth would have a gear ratio of $10/20 = 0.5$, or $0.5:1$. The output speed would then be $0.5$ times faster (so $2$ times slower) than the input speed.

## The relationship between the gear ratio and the speed ratio

The speed ratio is all about **angles**. The input and output gears interlock, and so they each rotate one tooth at a time, together.

- If the
**output gear has more teeth**than the input gear, the output gear has**a smaller angle between teeth**, resulting in a**lower rotational speed**on the output than the input. The gear speed ratio is lesser than 1. - If the
**output gear has fewer teeth**than the input gear, the angle between the output's teeth is**larger**, and the**output gear rotates faster**than the input. The gear speed ratio is greater than 1.

See the animation below: Having more teeth on the output (right) gear means a smaller angle to turn per tooth compared to the input (left) gear. This results in a gear speed ratio of <1, and a slower rotational speed on the output compared to the input.

### How do I calculate a vehicle's speed from its gear ratio?

To calculate the speed of the vehicle, follow these steps:

- Determine the engine's speed in rotations per minute (rpm). Consult the car's tachometer for this value.
- Multiply it with
`3.6 × π × r`

, where`r`

is the wheel radius in meters. - Divide it by
`30 × g`

, where`g`

is the gear ratio at the gearbox. - If the vehicle has a differential gear ratio, divide your result by it.

The result is the vehicle's speed in km/h.

### How do I calculate the speed ratio of gears?

The speed ratio is the inverse of the normal gear ratio. The **gear ratio** is the ratio of input teeth to output teeth (e.g., with 10 teeth on the input and 20 teeth on the output, the gear ratio is `10/20`

or `0.5 : 1`

. The **speed ratio** is the ratio of output speed to input speed (e.g., with a gear ratio of `0.5`

, the output speed will be `0.5`

that of the input speed).

### What is the speed ratio for a gear ratio of 0.5?

The output gear's speed will be ** 0.5 times as fast** (so

**) as the input's speed in a gear system with a total gear ratio of**

`2`

times as slow`0.5`

.