# Bike Speed Calculator

Created by Davide Borchia
Reviewed by Komal Rafay
Last updated: Feb 23, 2023

Omni's bike speed calculator will teach you how to calculate the bike speed you can achieve on your ride. You're in for a ride: keep reading to learn:

• The surprisingly easy math behind the calculations for bike speed;
• The formula to calculate bike speed from cadence; and
• The relevance of the proper gear ratio for your ride.

## The mathematics behind the speed of your bike: calculating the bike speed from cadence

A bike is a fascinating object. So simple, yet so versatile and fun. The operations of a bike can be translated into a simple "formula": rotation in, speed out.

Okay, we can explain this better. A bike is an efficient (the most efficient!) way humanity uses to transform a rotational motion (your beautiful pedaling legs) into a linear motion (your bike going fast). To do so, at first, cyclists were moving directly one of the wheels — think of penny-farthing. With the development of technology, gears were added to bikes, which allowed them to achieve higher speeds and lower strains.

The presence of only pedals, gears, and wheels between your quads and those sweet km/h allows us to understand the behavior of a bike with simple math. To calculate the bike speed, we use the following formula:

$s = \left(\pi \cdot \left(d + 2\!\cdot \!t\right)\right) \cdot \frac{n_{\text{chainring}}}{n_{\text{cog}}} \cdot c$

where:

• $s$ - The bike speed;
• $d$ - The wheel diameter;
• $t$ - The tire thickness (note that, we often include this value in $d$);
• $n_{\text{chainring}}$ and $n_{\text{cog}}$ - The number of teeth in the front and rear gears; and
• $c$ - The bike cadence.

As you can see, you can calculate the bike speed from the gear ratio and the cadence: the other parameters are more "fixed", and if you change them mid-ride, something wrong has happened.

## Let's understand the bike speed formula

The formula to calculate the bike speed from gears and cadence looks complex but is — in fact — easy to understand. We can "split" it into various elements, and all of them make sense: follow us!

1. With the first part of the equation, $\left(\pi \cdot \left(d + 2\cdot t\right)\right)$, you calculate the circumference of your wheel. The sum between brackets is the total diameter of the wheel.
2. Your wheels spin at a certain angular speed. Since we multiply the number of complete rotations of the wheel in a minute (its angular speed in $\text{RPM}$, or $1/\text{min}$) by the circumference of the wheel itself (corresponding to the distance covered by a single rotation), we find the speed of the bike as the distance traveled per minute.
3. Now, we need to calculate the angular speed of your bike. This quantity depends on the rotational speed of the crankset. How so? Through the gear ratio — the ratio between the number of teeth of chainring and cog —: the cadence (the rotation per minutes you impart to the crankset with your legs) times the gear ratio returns the rotational speed of the rear wheel.

That's it. Take a look at the formula, and follow the three steps: you will clearly see them and the role of each part of the formula.

## The importance of gear ratio in the calculations for the bike speed

The cadence and the gear ratio work synergically to determine how fast you are going: you can see it in our bike speed calculator by changing the two values and comparing the variation in speed.

The cadence you can sustain on your bike is a personal quantity. Chris Froome, for example, is a beast able to maintain extremely high cadences — even on climbs, at least when he's not running!

Your cadence should be comfortable: good values often fall between $60\ \text{RPM}$ and $100\ \text{RPM}$.

The gear ratio is fundamental to translating your cadence into speed. A high gear ratio (high gear in front, low gear in the back) helps you develop higher speed. At the same time, that ratio requires you to input a higher torque, which may result in muscular strain, fatigue, and, in general, an unpleasant ride.

A low gear ratio, on the other hand, corresponds to a less efficient way to translate the cadence into speed. However, the torque gets transmitted way better: that's why those ratios are ideal for your climbs.

Choose the best gear ratio for both the situation and your legs.

## Maths on two wheels: other bike calculator from speed to cadence

Omni loves bikes, and we think you can love them too. Try our car vs. bike calculator if you are not convinced.

Omni also loves science, and that's why we created a handy set of tools to help you on the saddle, not with tools, but with numbers. After our bike speed calculator, try our:

## FAQ

### How do I calculate the bike speed from the gear ratio?

To calculate the bike speed from the gear ratio and cadence, use the following formula:
s = (π × (d + 2t) × (Nchainring/Ncog) × c
Where you can find:

• s — The bike's speed;
• d and t — The wheel's diameter and the tire's thickness;
• Nchainring and Ncog — The number of teeth of your gear choice; and
• c — Your cadence.

### Which is the best cadence for a sprint?

To maximize the speed for your sprint, aim to achieve a cadence of 110 RPM. You won't be able to maintain this cadence for long, but with the right choice of gear, and adequate training, you'd be able to reach about 55 km/h.

### What is the bike speed for a cadence of 70 RPM on a 29" fixie?

You can reach 27 km/h. Assuming your 29" fixie has a standard gear ratio 2.75:1, pedaling with cadence c = 70 RPM , apply the formula for the bike speed:
s = (π × 0.74 m) × 2.75 × 70 RPM = 26.85 km/h

### Does higher gear mean faster bike?

Yes, but it also means higher strain. You can feel that using a higher gear ratio requires you to input more torque on the pedals. While you would make your rear wheel spin faster, your legs would also tire as quickly. Choose a lower gear in the back and train to achieve a constant higher cadence rather than a lower cadence with higher gears!

Davide Borchia
Wheel diameter
in
Tire size
in
Chainring
teeth
Cog
teeth
Gear ratio
:1
RPM
Speed
mph
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