Centrifuge Balance Chart

Format:

Why does balance matter?

A centrifuge can spin at tens of thousands of RPM. If your samples aren't arranged symmetrically, the rotor wobbles — creating vibrations that can damage the motor, crack tubes, and ruin your samples.

Every manufacturer prints a balance chart showing which tube counts are safe. This app generates those charts dynamically for any rotor size.

Unbalanced

Balanced

The building blocks: regular shapes

Here's the key insight: any regular polygon is perfectly balanced. If you place tubes at the corners of an equilateral triangle, they pull equally in every direction and cancel out. Same for a pair of opposite tubes, a pentagon, and so on.

Pair (n=2)

Two tubes directly opposite

Triangle (n=3)

Three equally-spaced tubes

Combined (n=5)

1 pair + 1 triangle

You can stack as many balanced shapes as you need — the combination stays balanced. That's how the algorithm builds every configuration on this chart.

What the colors tell you

Blue dots

These slots are part of a pair formation — two tubes directly across from each other. Also used for pentagons in 30-slot rotors.

Red dots

These slots are part of a triangle formation — three tubes equally spaced around the ring.

Cards that are all one color use only one type of shape. Mixed-color cards combine pairs and triangles.

Which numbers of tubes can be balanced?

This depends on the number of slots K. Specifically, it depends on K's prime factors — the prime numbers that divide evenly into K.

Rule: n tubes are balanceable if n can be built by adding together K's prime factors (with repetition).

K = 30 → primes: 2, 3, 5

n=6 = 2+2+2 ✓

n=7 = 2+2+3 ✓

n=9 = 3+3+3 ✓

n=1 = can't make it ✗

K = 24 → primes: 2, 3

n=4 = 2+2 ✓

n=5 = 2+3 ✓

n=9 = 3+3+3 ✓

n=1 = can't make it ✗

K = 10 → primes: 2, 5

n=2 = 2 ✓

n=4 = 2+2 ✓

n=3 = can't make it ✗

n=7 = can't make it ✗

Rotors with more prime factors (like K=30 with primes 2, 3, and 5) have more valid configurations. Rotors with fewer prime factors are more restrictive.

Impossible configurations (the × cards)

Some counts simply can't be balanced, no matter how you arrange them. The most common:

× n = 1: A single tube has nothing to counterbalance it. There's no polygon with just one point.
× n = K − 1: This is the "mirror" of n=1. One slot is always empty with no counterpart.

Some rotors have more impossible values — K=10 has four (n = 1, 3, 7, 9) because 3 and 7 can't be made from 2s and 5s.

n = 1

The full ring (n = K)

When every slot is filled, the rotor is trivially balanced — the weight is perfectly uniform in all directions. This is why the last card in any chart is always valid and shown in blue.

Generated live in your browser — no server involved. Coded with AI by Jon Ebueng, CIS @ HMC.