Bike Gear Calculator

A bike gear calculator will calculate various values, namely the gear ratio, chainwheel inches, circumference, gear inches and speed that a particular gear can achieve at a given cadence based on crankset, sprockets and wheel. By inputting one of these five values you can simultaneously display all the others. In planning mode it is also possible to work backwards from a desired target speed to determine which gear will be required. These calculations form the mathematical basis for selecting chainrings, determining crankset size and setting up fixed gears.

Five ways to measure translation

A single number alone cannot fully tell you how "big" a translation is, as each measure answers different questions. Four of them are about the translation itself while the fifth converts it into speed.

translation

The gear ratio is the simplest way to measure this and is calculated by dividing the number of teeth on the chainring by the number of teeth on the cog. This will tell you how many times the rear wheel turns for each pedal revolution.

If a 50 tooth chainring is paired with a 15 tooth cog the gear ratio is 3.33, as 50 divided by 15 equals 3.33. The wheel will turn 3.33 times for every revolution of the pedals. This is useful for comparing within the same bike but due to not taking into account tire size road bikes and mountain bikes cannot be directly compared with each other.

gearbox duty

The term gear ratio refers to an aspect of the wheels. It comes from the days of high wheel bicycles also known as penny-farthing. At that time a bicycle's gearing was actually based on the diameter of the drive wheel. Today it refers to the diameter of an older direct drive wheel which achieves the same gearing.

For example, a 700c wheel has a diameter of about 26.5 inches. At a gear ratio of 50/15 this is 88 inch-gears. Typical ratios on road bikes range from the high 20s (smaller chainrings) to around 125 (large chainrings, e.g. 53/11). Because the calculation takes into account wheel size, gear inches can be directly compared even between different bicycles. This is why this method has been used for over a century.

development or scope of work

The development indicates how far a bike goes in one complete revolution of the pedals. It is the product of the gear ratio and circumference of the wheel. Riders in countries that use the metric system often refer to this as "development" in meters. Mechanics measure this directly, calling it "rolling circumference". They do so by marking on the tire, moving the bike through one pedal revolution, then measuring the distance traveled.

If a 50/15 size cog is fitted to a wheel of size 700C then the bike will travel about 7.0 meters per pedal revolution. The roll-out distance is the most intuitive way to measure, and measuring your own wheels gives the most accurate data for this calculator as actual tire diameter varies with width and pressure.

Translation ratio

The gear ratio is a modern method of calculating the gearing that was popularized by bicycle expert Sheldon Brown. Both the gear ratio and effective gear size assume that crank length is constant. However, since longer cranks create more leverage, bicycles with the same gear ratio can have very different riding characteristics. The gear ratio solves this problem by first dividing wheel radius by crank length, then multiplying the gear ratio.

This is a pure number with no units that expresses the ratio of distance traveled to the path of the foot on the circumference of the pedal. A small gear ratio (2.0) means very easy pedaling for climbs, while values between 5 and 6 are comfortable all-round gears, whereas 9 or 10 is best for sprints. As it takes into account crank length, this is the fairest method to compare gear ratios of different bikes.

Speed and cadence

The multiplication of the effective gear size by the pedaling frequency results in the speed on the road. The pedal frequency is expressed in revolutions per minute (RPM), and most riders feel comfortable with a pedal frequency between 80 and 100 RPM.

A 50/15 gear ratio ridden at a cadence of 90 RPM results in a speed of about 38 km/h or 24 mph. This is why bike computers can display speed with just one wheel sensor, and why experienced riders shift gears up or down on the road to maintain a constant cadence.

A complete example:

Let's take a road bike with a two-speed gear system. It has a chainring with 50 teeth, a cassette with 15 teeth, a 700C wheel (with a 25mm wide tire), a crankshaft with a length of 170 mm and a pedaling frequency of 90 revolutions per minute. The outer diameter of the wheel is 622 mm, which is increased by twice the tire depth of 25 mm, so it's 672 mm, or 26.5 inches.

If you switch from the inner chainring with 34 teeth to a cassette with 32 teeth, the gear ratio of the bike changes to 1.06, the range becomes 28 and the transmission is 2.1. At the same pedaling frequency, you reach about 12 km/h. This is really an appropriate gear ratio for climbs.

The choice of translation ratio:

The numerical values of the gear ratio are not meant to be memorized but are best used for comparison purposes. When replacing a cassette or chainring, you should input the old and new settings into a calculator tool to check the change in gearing or range. If the difference between gears is less than about 10 percent points, shifting will feel smooth. With larger differences, either pedaling becomes light on every shift or heavy on every shift.

For the smaller cogs you should consider how long you can keep pedalling at a particular gear on the steepest climb in your area. For the larger ones you should check what speed the highest gear will achieve with a cadence that feels comfortable for you. If your legs are constantly spinning over when descending, then you're probably not making optimal use of your current ratio. In planning mode, you can calculate this in reverse. Enter the desired speed and it will show you suitable gears along with examples of chainring and cassette combinations which will achieve that speed.

Information about rim and tire sizes:

The wheel size listed here is determined by two factors: the inner diameter of the rim flange, which you select from a drop-down menu, and the tire width that you enter in addition to that. The numbers in parentheses after each rim option are the ETRTO inner diameter of the rim flange in millimeters. 622 refers to 700C and 29er, 584 is for 650B and 27.5 inch, and 559 is for classic 26 inch mountain bikes. The roll circumference is calculated by increasing the rim diameter by twice the tire width. This is because the tire sits on both sides of the rim.

These are approximate values. The actual measured tire width is slightly less than the nominal width and compresses under load. To get the most accurate values for rolling resistance and speed, measure your own track length and calculate the effective diameter from that or simply compare differences between two gears without focusing too much on absolute values.

This calculator is for reference information and planning equipment for bicycles. The actual speed will be affected by factors such as wind, gradient, rolling resistance and the rider's power but these cannot be derived from the gear ratio numbers.