ISO 21940-11 Balance Tolerance Calculator

Balance tolerance is the single most consequential number in a balancing specification, and it is the one most often chosen by habit. This page explains how ISO 21940-11 derives a permissible residual unbalance, and how to work the calculation yourself. The method is vendor-neutral: it applies whatever equipment does the measuring.

Open the ISO 21940-11 balance tolerance calculator — free, no registration.

What balance tolerance actually specifies

A rotor is unbalanced when its mass axis does not coincide with its shaft axis. The offset between them is the specific unbalance, written e and expressed in micrometres. Multiply that offset by the rotor mass and you get unbalance, U, expressed in gram-millimetres or ounce-inches.

No rotor is perfectly balanced. The question a specification answers is how much residual unbalance is acceptable, and ISO 21940-11 answers it by holding one quantity constant: the product of specific unbalance and angular velocity. That product has units of velocity, and it is the balance quality grade, G, given in millimetres per second.

This is why a grade alone is not a tolerance. G6.3 means something different for a 2 kg rotor at 12,000 rpm than for a 200 kg rotor at 900 rpm. The grade is the starting point; mass and service speed convert it into a number a machine can be set to.

Step 1 — Select a balance quality grade

ISO 21940-11 assigns grades by rotor type and service. The grades below are those offered in the calculator, with representative rotors from the standard.

Grade	Representative rotor types
G0.4	Precision grinding spindles, gyroscopes
G1	Grinding machine drives, tape and disc drives, small armatures with special requirements
G2.5	Gas and steam turbines, turbo-compressors, machine tool drives, turbine-driven pumps, small electric armatures
G6.3	Pump impellers, fans, flywheels, centrifuge drums, paper machine rolls, assembled aircraft gas turbine rotors, general machinery parts
G16	Drive shafts with special requirements, crushing and agricultural machinery parts, individual engine components
G40	Car wheels, wheel rims, wheel sets, drive shafts; crankshaft drives of elastically mounted four-cycle engines with six or more cylinders
G100	Crankshaft drives of fast diesel engines with six or more cylinders; complete engines for cars, trucks and locomotives
G250	Crankshaft drives of rigidly mounted fast four-cylinder diesel engines
G630	Crankshaft drives of rigidly mounted large two-cycle engines, slow marine diesel engines

Where a customer drawing or an industry specification already names a grade, use it. Where nothing is specified, the standard’s rotor-type table is the defensible starting point — and the grade should be agreed before tooling is designed, not after.

Step 2 — Convert the grade into permissible residual unbalance

Because G is the product of specific unbalance and angular velocity, the permissible specific unbalance follows directly:

e_per = (G × 60) ÷ (2π × n)

  e_per  permissible specific unbalance, mm
  G      balance quality grade, mm/s
  n      service speed, rpm

Expressed in micrometres and combined with rotor mass, this reduces to the working form:

U_per = (9549 × G × m) ÷ n

  U_per  permissible residual unbalance, g·mm
  G      balance quality grade, mm/s
  m      rotor mass, kg
  n      service speed, rpm

Two consequences are worth internalising. Tolerance scales linearly with mass, so a heavier rotor at the same grade and speed is allowed proportionally more residual unbalance. And tolerance is inversely proportional to speed, so doubling service speed halves the permissible unbalance. High-speed rotors are demanding not because they are harder to measure but because the standard allows them less.

Step 3 — Allocate the tolerance between correction planes

The figure from Step 2 is the permissible unbalance for the rotor as a whole. A disc-shaped rotor corrected in one plane takes the full value. A rotor requiring two-plane correction has that value distributed between the planes.

For a symmetric rotor with correction planes near the bearings, an equal split between planes is the common case. For asymmetric rotors, rotors with overhung mass, or planes set well inboard of the bearings, ISO 21940-11 gives allocation rules based on the geometry — and the split is not equal. Applying a blanket halving to an asymmetric rotor produces a tolerance that is too loose on one plane and too tight on the other.

Worked example

A cast pump impeller, balanced in two planes, running at motor speed:

Balance quality grade: G6.3 (pump impeller, per the table above)
Rotor mass: 18 kg
Service speed: 1780 rpm
Correction planes: 2, symmetric

Permissible specific unbalance:

e_per = 9549 × 6.3 ÷ 1780 = 33.8 µm

The mass centre may sit up to 33.8 µm off the shaft axis. Multiplying by rotor mass:

U_per = 9549 × 6.3 × 18 ÷ 1780 = 608 g·mm  (0.845 oz·in)

Per plane (symmetric, two planes):
        304 g·mm  (0.42 oz·in)

Change one input to see how the specification moves. At 3560 rpm rather than 1780, the same impeller at the same grade is allowed 304 g·mm total — half as much. At G2.5 rather than G6.3, it is allowed 241 g·mm. Neither change touches the part; both change what the machine must be capable of resolving.

Unit conversions

Balance tolerances are quoted in gram-millimetres in most of the world and ounce-inches across much of North American industry. The calculator handles the conversion, but the factors are worth knowing:

From	To	Multiply by
oz·in	g·mm	720
g·mm	oz·in	0.001389
g·cm	g·mm	10
kg·mm	g·mm	1000

Mixing the two is a common and expensive error. A tolerance written as 600 without units is 600 g·mm or 432,000 g·mm depending on who reads it.

What the calculation does not decide

ISO 21940-11 gives you a target. It does not tell you whether a given machine and tooling combination can hold it on your part.

Machine class must carry tooling weight plus part weight, and tooling is not known until part prints are reviewed and a fixture concept exists. The heavier the part-plus-tooling combination sits relative to the machine’s class, the less repeatable and accurate the measurement becomes. A tolerance that is arithmetically correct can still be unachievable on an undersized machine, and the same part can be straightforward on a properly sized one. See BTI’s platforms and classes for how a machine is sized against what you need to prove.

Part geometry matters as much as the number. Rotors with their own spindles, thin-walled castings, flexible shafts, and assemblies whose components shift during handling all behave differently from a rigid rotor on a mandrel. Capability has to be evaluated for the specific part and process rather than assumed from the tolerance alone.

Working without an original specification

This is the common case on remanufactured, aftermarket, and repaired parts: there’s no drawing calling out a grade, because the part was never balanced against one in the first place, or the paperwork didn’t survive. The rotor-type table above is a reasonable starting point, but it can’t account for how a specific part actually behaves — whether it stays rigid at service speed, how repeatably its locating features seat, or what an assembly does that the bare rotor doesn’t.

BTI’s Measurement & Testing division characterizes parts like this directly and establishes acceptance criteria against actual behavior rather than an assumed grade. Where you need to know what’s achievable before committing to a machine, that’s the question it’s built to answer.

Frequently asked questions

Which speed do I use — service speed or balancing speed?

Service speed, the maximum speed the rotor sees in operation. Balancing speed is a property of the machine and process; it does not enter the tolerance calculation. A rotor balanced at 900 rpm on a soft-bearing machine is still specified against the speed it will run at in service.

What if my rotor runs across a speed range?

Use the maximum service speed. It produces the tightest tolerance, and a rotor that satisfies it satisfies the rest of the range.

Does the mass include tooling, shafts, or the mandrel?

Rotor mass in the calculation is the mass of the rotating assembly as it runs in service. Balancing tooling and mandrels are not part of the rotor and do not enter the tolerance, though they very much affect whether the tolerance can be measured repeatably.

One plane or two?

Broadly, a rotor whose axial length is short relative to its diameter behaves as a disc and can be corrected in a single plane. Longer rotors develop couple unbalance that a single plane cannot correct, and require two. Where the geometry sits near the boundary, the deciding factor is usually whether single-plane correction leaves residual couple unbalance above tolerance.

Is a finer grade always better?

No. Specifying a grade tighter than the application needs raises machine class, cycle time, and cost without changing how the part performs. The standard’s rotor-type table exists because those grades reflect what the service condition actually requires.

Related resources

Questions about applying a grade to a specific part, or sizing a machine to a tolerance you already hold? Contact BTI — reviewing part prints is the first step either way.