Calculate pulley size or RPM from a motor pulley’s diameter and speed, with the pulley ratio, belt speed and an optional belt length estimate.
Pulley Size Formula
The core relationship for an ideal two-pulley belt drive is equal belt speed at the pitch/effective circumference of both pulleys, assuming no slip. This gives the fundamental equation:
Where D1 is the driver pulley pitch/effective diameter, N1 is the driver pulley RPM, D2 is the driven pulley pitch/effective diameter, and N2 is the driven pulley RPM. Use the same diameter basis and length unit for both pulleys. Rearranging to solve for the driven diameter:
This equation assumes zero belt slip. A friction belt may run at a different speed under load because of creep or slip; the amount depends on the belt, tension and operating conditions. Synchronous timing belts use toothed engagement, but still require manufacturer checks for the intended speed and load.
Pulley Ratio, Speed, and Torque
Here the reduction ratio is the driven diameter divided by the driver diameter: Ratio = D2 / D1 = N1 / N2, assuming no slip. A ratio greater than 1 means the driven shaft turns slower; a ratio less than 1 means it turns faster. The power relationship is P = T × ω, with power in watts, torque in newton-metres and angular speed in radians per second. Ignoring losses, halving speed doubles torque at the same transmitted power. Real output torque also depends on drive losses, which this calculator does not estimate.
For example, a 1,750 RPM motor with a 4-inch driver pitch diameter and an 8-inch driven pitch diameter has a 2:1 reduction ratio. The ideal driven speed is 875 RPM. If the driver supplies 10 N·m, the ideal output torque is 20 N·m before drive losses.
Belt Length Between Two Pulleys
Once you know both pitch/effective diameters and the centre distance between shafts, estimate the pitch-line length of an open belt around two coplanar pulleys, without idlers or a crossed belt, using this approximation:
Where L is the approximate pitch-line belt length, D1 and D2 are the pulley pitch/effective diameters, and C is shaft centre distance, all in the same length unit. The half-circumference and 2C terms give the leading length estimate; the final term corrects for unequal diameters. For equal diameters, the geometric length is L = πD + 2C. The approximation becomes less accurate as the diameter difference becomes large relative to centre distance. Non-overlapping pitch circles require C > (D1 + D2)/2; actual outside diameters and flanges need additional clearance checks. Select the standard belt length and installation/tension adjustment using the belt manufacturer's method.
Minimum Pulley Diameters by V-Belt Cross Section
A pulley that is too small for the selected belt can increase bending stress and reduce belt life. Minimum diameters depend on the specific belt product, profile and operating conditions. Use the manufacturer's selection tables rather than a universal minimum for all belts with a similar section name:
| Selection check | Manufacturer information to use |
|---|---|
| Belt product and profile | Exact belt series, section and compatible pulley groove |
| Smallest pulley | Recommended diameter and its pitch, datum or outside-diameter basis |
| Speed and load | Permitted operating speed, power rating and service factors |
| Installation | Wrap, tension, clearance and centre-distance adjustment requirements |
These checks are specific to the selected product and application. A calculated speed ratio or belt length does not establish a safe minimum pulley diameter, expected service life or warranty coverage; verify those points in the applicable manufacturer documentation.
Belt Drive Efficiency and Slip
Belt-drive efficiency depends on the belt construction, pulley sizes, load, tension, alignment and operating conditions. Flexing and friction consume power. Synchronous belts use toothed engagement to maintain the intended ratio, but they still have drive losses. Use product-specific manufacturer data when efficiency is needed; this calculator applies the ideal no-slip speed relation.
In a friction belt, elastic stretch and recovery can cause creep. Gross slip can occur when tension or traction is inadequate for the load, leading to heat and wear. Adequate wrap, correct tension and alignment must be checked using the selected belt's design and maintenance instructions; no fixed slip allowance is applied here.
Common Applications and Typical Pulley Sizes
Pulley sizing varies by application. HVAC blowers and compressors use pulley ratios to match the required equipment speed and load. Workshop machinery such as drill presses and lathes may use step pulleys to select different speed ranges. Choose actual diameters and belts from the equipment and belt manufacturers' specifications.
In automotive applications, pulley ratios set the speeds of the alternator, water pump and other belt-driven accessories relative to the crankshaft. Use the vehicle and accessory manufacturers' pulley specifications, output-versus-speed data and maximum speed limits. A single RPM threshold does not establish rated output for every alternator.
Compound (Multi-Stage) Pulley Systems
When a single pulley pair cannot achieve the required speed ratio without an impractical diameter, a compound drive can use two pulleys on an intermediate shaft. One is driven by the motor; the other drives the final output. The ideal overall reduction ratio is the product of the stage ratios. For example, a 3-inch driver and 9-inch driven pulley (3:1), followed by a 3-inch driver and 12-inch driven pulley (4:1), produce 12:1 overall. With consistent pitch/effective diameters and no slip, 1,750 RPM becomes approximately 146 RPM. Each stage still requires its own belt, pulley, load and clearance checks.
Pitch Diameter vs. Outside Diameter
Use the manufacturer's specified pitch, datum or effective diameter basis consistently for the selected belt and pulley. The speed relationship follows the belt's effective running circumference, which need not equal the pulley outside diameter measured with calipers. The appropriate conversion depends on the belt profile and pulley specification; do not apply a universal outside-diameter offset. Mixing diameter bases can give an incorrect speed ratio or belt length.
