Calculation
i = d2 / d1
Diameter ratio sets speed; slip and belt stretch reduce real ratio.
i = d2/d1
Belt Drive Ratio Calculator
Diameter ratio sets speed; slip and belt stretch reduce real ratio.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Drive ratio i — The ideal belt-drive ratio – the ratio of pulley diameters, or equivalently of the ideal speeds with no slip.
- Driving pulley d1 — The pitch diameter of the driving pulley (the one on the motor/input side). Source: a drawing, or a calliper at the pulley's belt groove.
- Driven pulley d2 — The pitch diameter of the driven pulley.
Example
100/200 mm gives i = 2 and ideally halves output speed.
Assumptions and limits
No slip; use pitch, not outside, diameter.
Understand Belt Drive Ratio Calculator
This calculator finds the missing quantity among ratio i and pulley diameters d1 and d2 from the other two, for a belt drive. It explains why real output speed usually falls somewhat below the ideal calculated value because of belt slip.
What does this quantity describe?
For a two-pulley belt drive, ratio follows the pitch-diameter ratio: i = d2/d1. A larger driven pulley relative to the driving pulley correspondingly lowers output speed.
A V-belt between a motor pulley and a fan pulley works on the same principle as a bicycle chain: differently sized pulley diameters convert rotational speed. Unlike a rigid gear connection, though, a belt transmits force through friction, which creates a small amount of slip between belt and pulley under load.
Formula and variables
i = d2 / d1
i = d2 / d1d2 = i · d1d1 = d2 / i
| Symbol / input | Meaning |
|---|---|
| Drive ratio i | The ideal belt-drive ratio – the ratio of pulley diameters, or equivalently of the ideal speeds with no slip. |
| Driving pulley d1 | The pitch diameter of the driving pulley (the one on the motor/input side). Source: a drawing, or a calliper at the pulley's belt groove. |
| Driven pulley d2 | The pitch diameter of the driven pulley. |
Choose the inputs correctly
Enter two of the three quantities. Ratio requires both diameters, a sought diameter requires the ratio and the other diameter. Use the pulleys' pitch diameters, not their outside diameter.
How to use the calculator
Select the target quantity and enter the two known values with units. For real output speed, additionally account for the small slip typical of a properly tensioned V-belt.
Worked example
Given d1 = 100 mm and d2 = 200 mm, substitution gives i = 200/100 = 2. Ideal output speed is therefore halved relative to input speed.
Understand the result and units
A ratio of i = 2 means the driving pulley turns twice for every single turn of the larger driven pulley. Unlike a gear ratio, this value is an ideal upper bound rather than an exact real speed, because of possible belt slip.
Pulley diameters are given in mm; ratio i is a dimensionless ratio.
Typical applications
Belt ratios are used for fan drives, compressors, machine tool spindles, washing machine drums, and combustion-engine accessories such as alternators and water pumps.
Assumptions, limits and common mistakes
The formula assumes ideal, slip-free force transmission through the belt. Real belt drives additionally show creep (elastic-stretch slip from the belt's deformation as it transfers force) and, under overload, true slip; in well-designed drives, total speed loss usually stays within a few percent.
Common mistake: Do not confuse pitch diameter with the pulley's outside diameter — the ratio calculation depends on the diameter the belt effectively rides on. Also, do not neglect real slip under very high load, since it lowers actual output speed below the ideal calculated value.
Frequently asked questions
Why does real output speed differ from the calculated value?
Because of elastic stretch (creep) and, under high load, true slip between belt and pulley. Both slightly lower real speed below the ideal calculated value.
How much slip is typical for V-belts?
For properly tensioned drives, usually within a few percent, though heavily loaded exceptions can show noticeably more.
Does the outside diameter or the pitch diameter of the pulley count?
The pitch diameter, on which the belt effectively runs, counts for the ratio calculation — not the pulley's plain outside diameter.