Elevator counterweight and balance calculator

Counterweight mass from the empty car mass, the rated load and the balance ratio, with the out of balance empty and full and the largest out-of-balance force the machine holds.

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Result

Counterweight mass: 4,233 lb
Car load at balance: 1,587 lb
Out of balance, car empty: 1,587 lb
Out of balance, car fully loaded: 1,940 lb
Largest out of balance: 1,940 lb
Largest out-of-balance force: 1,940 lbf

Not engineering advice; a licensed professional checks every result. Not a substitute for a licensed engineer, the manufacturer's data or the authority having jurisdiction; confirm the code edition your jurisdiction has adopted. Textbook statics with no code limit, so no trade check is pending for this calculator. Terms of use and estimate disclaimer.

Drawing

Car and counterweight over the drive sheave, drawn to the same mass scale. The dashed block is the rated load.

Out of balance as the car fills: counterweight side heavier below the balance point, car side heavier above it.

Working

Counterweight mass: the empty car plus the balanced share of the rated load
$W = P + qQ$
W = 1200 + 0.45 × 1600 ≈ 1920 kg
= 1920 kg
Car load at which car and counterweight balance
$x_b = qQ$
x_b = 0.45 × 1600 ≈ 720 kg
= 720 kg
Out of balance with the car empty (counterweight side heavier)
$U_0 = W - P = qQ$
U_0 = 1920 − 1200 ≈ 720 kg
= 720 kg
Out of balance with the rated load in the car (car side heavier)
$U_Q = P + Q - W = (1 - q)Q$
U_Q = 1200 + 1600 − 1920 ≈ 880 kg
= 880 kg
Largest out-of-balance force the machine holds
$F = g \max(U_0, U_Q)$
F = 9.80665 × 880 ÷ 1000 ≈ 8.6299 kN
= 8.63 kN

Working is shown in the units each formula is written in; the result figures above follow the unit switch. A numeric input is taken to 15 significant digits before it is used (1033.2293579541322 kg is used as 1033.22935795413 kg); every echo of it shows that value, and a computed figure substituted into the working is quoted to 15 significant digits as well.

Notes

A balance ratio of 0.5 would make the empty and full out of balance equal (800 kg each); a lower ratio favours a lighter counterweight and a car that is usually part loaded.
Hoist ropes, the travelling cable and any compensating chain or rope also move weight between the two sides as the car travels; they are left out here. The manufacturer sets the final counterweight and the filler weights on site.
No elevator code fixes the balance ratio; it is a design choice. The typical 0.40 to 0.50 range is provisional, pending trade or textbook confirmation. The code does require the traction, the brake and the machine to handle the out of balance shown, which the designer checks separately.
Converted US input values are rounded for display only. The calculation keeps the SI values until you edit a field.

Method

What the counterweight does

A traction elevator hangs the car on one side of the drive sheave and a counterweight on the other. The counterweight carries the weight of the empty car plus a share of the rated load, so the motor only has to lift the difference. That share is the balance ratio.

With a balance ratio q, the counterweight mass is W = P + qQ, where P is the empty car mass and Q is the rated load. The car and the counterweight balance when the load in the car is qQ.

Out of balance, empty and full

With the car empty, the counterweight side is heavier by qQ. With the rated load in the car, the car side is heavier by (1 − q)Q. The larger of the two is what the brake, the traction and the machine have to hold, so a ratio of 0.5 gives the smallest worst case. The typical 0.40 to 0.50 range is provisional, pending trade or textbook confirmation; passenger cars spend much of their time part loaded.

What it leaves out

The hoist ropes, the travelling cable and any compensation move weight from one side to the other as the car travels, and they are not included. No code clause sets the balance ratio, so none is cited; the derivation is in the calculator's spec file.

Formulas

Counterweight mass

W = P + q Q

W = P + qQ

Out of balance, car empty

U_0 = q Q

U_0 = qQ

Out of balance, rated load in the car

U_Q = (1 - q) Q

U_Q = (1 - q)Q

Largest out-of-balance force

F = g max(U_0, U_Q), g = 9.80665 m/s²

F = g \max(U_0, U_Q)

Code basis: clause and edition

Standard	Edition	Clause	What it covers
Traction elevator statics (textbook balance-ratio method)	n/a	Derivation in this calculator's spec	Counterweight mass and out of balance from car mass, rated load and balance ratio

Rules are restated in our own words and computed for your inputs; no table or text from a standard is reproduced. The adopted edition varies by jurisdiction, so confirm the one your authority having jurisdiction enforces.

Inputs

Input	Unit	Range	Default
Empty car mass `carMass`	kilograms (kg)	100 to 20000	1200
Rated load `ratedLoad`	kilograms (kg)	50 to 13500	1600
Balance ratio `balance`		0.25 to 0.75	0.45

Worked examples

Each example below is a test the calculator must pass before it ships. The expected values were worked out by a separate implementation.

Example	Expected result (each in its declared unit)
1200 kg car, 1600 kg rated load, balance 0.45	counterweightMass: 1920 kg, balancedLoad: 720 kg, unbalanceEmpty: 720 kg, unbalanceFull: 880 kg, maxUnbalance: 880 kg, maxUnbalanceForce: 8.63 kN
2000 kg car, 2500 kg rated load, balance 0.5 (equal out of balance)	counterweightMass: 3250 kg, balancedLoad: 1250 kg, unbalanceEmpty: 1250 kg, unbalanceFull: 1250 kg, maxUnbalance: 1250 kg, maxUnbalanceForce: 12.26 kN
900 kg car, 630 kg rated load, balance 0.4	counterweightMass: 1152 kg, balancedLoad: 252 kg, unbalanceEmpty: 252 kg, unbalanceFull: 378 kg, maxUnbalance: 378 kg, maxUnbalanceForce: 3.71 kN
Heavy freight car: 3500 kg car, 4500 kg rated load, balance 0.55	counterweightMass: 5975 kg, balancedLoad: 2475 kg, unbalanceEmpty: 2475 kg, unbalanceFull: 2025 kg, maxUnbalance: 2475 kg, maxUnbalanceForce: 24.27 kN

For AI agents

This calculator is also the MCP tool elevator_counterweight at https://elevatorcalc.com/api/mcp, using the same function as this page. See how to connect, the llms.txt file, or the JSON catalogue.