3 Piece Wheel Calculator - Calculator Academy

Enter the radius, arc length per piece, or chord length per piece into the calculator to determine the missing measurement.

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3 Piece Wheel Calculator Formula

The following equations are used to calculate the missing measurement.

Arc = (2pi/3)\times r Chord = r\times \sqrt{3}

Where r is the radius of the wheel.
Arc is the arc length per piece of the wheel.
Chord is the chord length per piece of the wheel.

To calculate the missing measurement, input two values and leave the third field empty.

What is a 3 Piece Wheel Calculator?

Definition:

A 3 Piece Wheel Calculator is a tool that determines one missing geometric measurement (radius, arc length per piece, or chord length per piece) for a wheel divided into three equal sections, each spanning 120°.

How to Calculate with the 3 Piece Wheel Calculator?

Example Problem:

The following example outlines the steps and information needed to calculate the missing measurement.

First, determine which measurement is missing. In this example, the arc length is left empty.

Next, input the known values. For instance, the radius is provided as 10 units and the chord length as approximately 17.3205 units.

Finally, calculate the missing arc length using the formula above:

Arc = (2π/3) × 10

Arc ≈ 20.94395 units

FAQ

What happens if more than one field is left empty?

The calculator requires exactly one empty field so that it can accurately compute the missing measurement.

Can this calculator be used for wheels with a different number of pieces?

This calculator is specifically designed for a wheel divided into three equal pieces, each covering 120°.

What measurement units should I use?

Make sure all input values use the same unit system to ensure consistent and accurate results.

Follow-Up Calculations

If your 3-piece build comes out to an 18x10 wheel, the wider tire package it usually carries can be harder to balance cleanly than a narrow factory setup. You can figure out bead weight for wide tires so the assembly stays smooth at highway speed and doesn’t develop a shimmy after a few hundred miles.

A custom 20x12 wheel still has to support the same corner weight as the vehicle, so a front axle carrying about 2,800 lb means each wheel may see roughly 1,400 lb before bumps and potholes are added in. It helps to check the load each wheel must carry because the finished wheel should always be rated comfortably above the heaviest real-world corner load.

If your finished 3-piece setup weighs 34 lb instead of a stock 24 lb wheel, that extra 10 lb at each corner adds up to 40 lb of unsprung mass for the suspension to control. You can estimate the weight added at each corner to see why lighter wheels usually ride better, respond faster to bumps, and reduce strain on springs and dampers.