Pulley Calculator
Quickly work out driven pulley speed, required pulley diameter, belt speed, and mechanical advantage for a two-pulley belt drive.
Pulley Drive Guide
Pulley Calculator: Speed Ratio, Diameter Sizing, and Belt Drive Basics
This guide explains how the Pulley Calculator works, what its equations assume, and how to use the results for real belt/chain drive design. You’ll learn the core speed–diameter relationship, how to pick the right method, what variables matter most, and how to sanity-check your design with worked examples.
Quick Start
The Pulley Calculator on this page is built for two-pulley belt/chain drives where a driver pulley (connected to a motor) turns a driven pulley (connected to a load). It assumes an ideal drive unless you intentionally add slip/efficiency in your own design checks.
- 1 Decide what you need: driven speed \(N_2\) or driven diameter \(D_2\). Pick that in the Solve For dropdown.
- 2 Enter the driver speed \(N_1\) (rpm). Use the motor nameplate speed or measured shaft speed.
- 3 Enter the driver pulley pitch diameter \(D_1\). Pitch diameter is the effective belt contact diameter, not the outer rim.
- 4 If solving for \(N_2\): enter the known driven diameter \(D_2\).
- 5 If solving for \(D_2\): enter your target driven speed \(N_2\).
- 6 Review the Quick Stats (speed ratio, mechanical advantage, belt speed) to confirm the result is realistic.
- 7 Toggle Show Steps to see the substituted equations and verify your inputs.
Tip: If you don’t know pitch diameter, use nominal pulley diameter as a first pass, then refine from the pulley catalog.
Common mistake: Mixing outside diameter with pitch diameter can shift ratios by several percent, especially on small pulleys.
Scope note: This calculator is for rotating belt/chain drives. For block-and-tackle lifting pulleys, mechanical advantage comes from rope segments rather than diameter ratios.
Choosing Your Method
In practice, there are a few ways engineers size pulley drives. The calculator uses the standard ideal relationship, but you should choose the method that matches your design stage and accuracy needs.
Method A — Ideal Speed Ratio (Calculator Method)
Use this for quick sizing, classroom problems, or well-tensioned drives with negligible slip.
- Fast and algebraic—no iteration required.
- Works for V-belts, flat belts, timing belts, and chain drives as a first approximation.
- Best when you need a diameter quickly to hit a target speed.
- Ignores slip, belt creep, and efficiency losses.
- Doesn’t check wrap angle or belt speed limits.
Method B — Ideal Ratio + Slip / Efficiency
Use this when the drive is near its torque limit or operates in dusty/oily conditions.
- More realistic for high-load V-belt drives.
- Lets you “back out” expected speed droop under load.
- Slip values are empirical and vary with tension, wear, and environment.
- Still not a full belt selection workflow.
Method C — Power-Based Drive Selection
Use this for final design: select belt type/quantity from manufacturer charts using power and speed.
- Checks belt rating, wrap angle correction, service factor, and life.
- Reduces the chance of overheating or premature belt failure.
- Requires torque/power data and a catalog workflow.
- More time-consuming than ratio sizing.
A good workflow is: (1) use the calculator for ratio/diameter, (2) sanity-check belt speed and torque multiplication, then (3) validate the belt or chain selection with catalog power ratings.
What Moves the Number
Pulley drives look simple, but a handful of variables control the result and whether the design behaves well in the field.
This is the main lever. Larger \(D_2\) relative to \(D_1\) reduces speed and increases torque. Smaller \(D_2\) increases speed but can create high belt speed and low wrap angles.
The output scales linearly with \(N_1\). If \(N_1\) can vary (VFDs, engines, wind), size for worst-case speed.
Using outside diameter can slightly over-predict speed reduction. Pitch diameter is the belt’s true radius of action.
V-belts can lose 2–5% speed under load if tension is low or the belt is worn. Timing belts and chains are near-zero slip.
High belt speed increases power capacity but can exceed belt ratings, raise noise, and amplify imbalance. Catalogs usually specify a recommended max \(v\).
Small driver pulleys reduce wrap angle and can cause slip. Increasing center distance or adding an idler improves wrap.
Design intuition: If you need big speed reduction, consider multi-stage pulleys rather than one extreme ratio that forces a tiny driver pulley.
Worked Examples
These examples mirror the calculator’s two Solve For options. Numbers are realistic for common shop and industrial drives.
Example 1 — Solve for Driven Speed \(N_2\)
- Driver speed: \(N_1 = 1200\ \text{rpm}\)
- Driver diameter: \(D_1 = 150\ \text{mm}\)
- Driven diameter: \(D_2 = 300\ \text{mm}\)
- Drive type: V-belt, well-tensioned (assume negligible slip)
The speed ratio is \(i = N_1/N_2 = 1200/600 = 2\). That implies roughly a 2× torque multiplication at the driven shaft (ignoring losses), which matches the calculator’s mechanical advantage quick stat.
Example 2 — Solve for Driven Diameter \(D_2\)
- Driver speed: \(N_1 = 1750\ \text{rpm}\)
- Target driven speed: \(N_2 = 900\ \text{rpm}\)
- Driver diameter: \(D_1 = 4\ \text{in}\)
- Drive type: Timing belt (no slip)
In real hardware you would choose a nearby standard pitch diameter, say 7.5 or 8.0 in, and accept a small speed difference. The quick stats belt speed helps you verify the chosen driver pulley won’t exceed the belt’s linear speed rating.
Common Layouts & Variations
The calculator covers the core two-pulley ratio. Here are typical configurations you’ll see in the field and how they affect design choices.
| Configuration | Typical Use | Pros | Cons / Notes |
|---|---|---|---|
| V-belt, open drive | General industrial power transmission | Cheap, tolerant of misalignment, good shock absorption | 2–5% slip possible; check tension & wrap angle |
| Timing belt | Precision speed/positioning | No slip, accurate speed ratio, low maintenance | Needs good alignment; no overload slip protection |
| Chain drive | High torque, harsh environments | Near-zero slip, compact, strong | Noisy, needs lubrication; polygonal speed variations |
| Multi-stage reduction | Large speed reductions (e.g., 10:1+) | Uses moderate ratios per stage, better wrap angles | More components; compound losses |
| Idler pulley added | Improve wrap / tensioning | Reduces slip, increases belt contact | Extra bearing losses; must be sized for belt load |
| Step pulleys | Discrete speed changes (lathes, drills) | Simple speed selection | Ratio depends on matching step diameters carefully |
- Prefer driver pulleys above the catalog minimum diameter for your belt type.
- Keep ratios per stage reasonable (often < 6:1) to maintain wrap and belt life.
- Account for torque spikes with a service factor, not just steady power.
- Guard rotating belts and pulleys per safety codes.
Specs, Logistics & Sanity Checks
The calculator gives the ratio result, but a robust pulley design needs a few extra checks before you order hardware or release drawings.
Check Belt Speed
Belt linear speed from the driver is: \[ v = \frac{\pi D_1 N_1}{60} \] Many V-belt catalogs recommend keeping \(v\) below roughly 25–30 m/s depending on belt section. If your belt speed is high, use a larger driver pulley or a slower motor with more reduction.
Wrap Angle & Tension
Small driver pulleys reduce wrap angle and friction. If you’re close to a torque limit, increase center distance, add an idler, or move to a toothed belt/chain.
A good rule of thumb: keep driver wrap angle above ~120° for V-belts when possible.
Pulley Materials
Cast iron and steel pulleys handle heat and wear well for industrial drives. Aluminum reduces inertia in high-speed machines but can wear faster with abrasive dust. For plastic pulleys, confirm temperature range and creep resistance.
Alignment & Runout
Misalignment increases belt wear and creates speed irregularity that the ideal equation can’t predict. Use straightedges/laser alignment and verify pulley runout before commissioning.
Service Factor
Size belts and shafts for real duty: starts/stops, shock loading, and ambient temperature. A 1.2–1.5 service factor is common before selecting belts by catalog power ratings.
Reality Check
Ask: does the new speed fit the machine’s safe operating range? If a fan or pump is involved, remember affinity laws: power can scale roughly with \(N^3\), so a “small” speed change can blow up power demand.
Safety: Exposed pulleys are a pinch/entanglement hazard. Always design guards and follow your site’s lock-out/tag-out procedure during maintenance.