How to use the pulley and belt calculator
Use this tool to compare the ideal speed relationship of two pulleys and calculate the geometric path length of an open belt. It suits a quick dimensional check or an educational belt-drive example. It does not select a catalog belt or determine a tension setting. The driver is connected to the input shaft; the driven pulley is the output.
- Enter the driver diameter D₁, driven diameter D₂ and center distance C in millimeters. Enter full diameters, not radii. Measure the center distance between the two shaft centers, not the gap between pulley edges. All three dimensions must describe the same belt contact line. Then enter the driver speed in RPM and press Calculate or Enter.
- The result gives total geometric belt length, input-to-output speed ratio, driven RPM and the length of one straight belt span. The diagram identifies D₁, D₂ and C and connects the pulleys with external tangents and contact arcs. Any input edit updates the live drawing when valid and clears the confirmed result. Clear empties the numeric inputs; calculate again after entering a fresh set.
The exact open-belt geometry
Let R = max(D₁, D₂) / 2, r = min(D₁, D₂) / 2 and Δ = R − r. The tangent angle is α = asin(Δ / C), in radians. One straight span is s = √(C² − Δ²). The two spans and the wrapped arcs add to L = 2s + π(R + r) + 2Δα.
This calculator uses that geometric equation rather than the common small-angle approximation L ≈ 2C + π(D₁ + D₂) / 2 + (D₁ − D₂)² / (4C). With equal diameters, Δ is zero and the exact equation reduces to L = 2C + πD. The result refers to the chosen contact line of an ideal belt with no thickness or stretch.
With no slip, both pulleys have the same belt surface speed: n₁D₁ = n₂D₂. Therefore n₂ = n₁D₁ / D₂ and the input/output ratio is D₂ / D₁. An open belt gives the same rotation direction at both pulleys. Animation uses clockwise input and a slowed display that preserves relative pulley speeds.
Two worked examples
Equal pulleys: D₁ = D₂ = 100 mm, C = 300 mm and input = 1,200 RPM give a 1 : 1 ratio and 1,200 output RPM. Each straight span is 300 mm; total length is 600 + 100π = 914.16 mm after rounding. A ratio of one preserves ideal speed even if the center distance changes.
Reduction: D₁ = 100 mm, D₂ = 200 mm, C = 400 mm and input = 1,200 RPM give 2 : 1, 600 output RPM, about 396.86 mm per straight span and 1,277.50 mm total belt length. Swapping the two diameters leaves the belt length unchanged but changes the speed ratio to 0.5 : 1 and output to 2,400 RPM.
Dimensions, errors and using the result
Dimensions must be positive and no greater than 1,000,000 mm. Input speed may range from zero to 1,000,000,000 RPM. C must be greater than (D₁ + D₂) / 2: this stricter physical condition keeps the pulley circles from touching or overlapping. An error beside the center-distance field means the shafts must be farther apart or the diameters smaller.
Use a decimal point or comma with no thousands separators or unit suffixes. Scientific notation is accepted. Results are rounded only for display, normally to two decimal places with trailing zeros removed; tiny nonzero values use scientific notation. The drawing compresses extreme proportions to keep both pulleys visible, so read the numerical dimensions instead of measuring the screen.
Copy result places the displayed results and dimension labels on the clipboard as plain text. Keep that text with your own input record if comparing alternatives. No file is saved automatically, and changing language reloads the form. This geometric length alone does not determine a purchasable belt size: manufacturer pitch-length conventions, belt section, thickness and installation adjustment can change the relevant dimensions.
Frequently asked questions
Can I enter a radius?
Double the radius first and enter the diameter. Entering a radius as a diameter halves that pulley’s modeled size and changes both belt length and speed ratio.
Does this support crossed belts?
No. A crossed belt uses internal tangents and reverses rotation. This tool models an open, uncrossed belt only.
Why can the belt length stay the same when I swap pulleys?
Length depends on both sizes and their separation, not which shaft supplies power. Speed depends on which pulley is the driver, so the RPM result changes when the diameters are swapped.
Can this determine belt tension or select a component?
No. Tension, transmitted power, friction, wrap requirements, alignment and rated speed are not calculated. Use the relevant manufacturer’s dimensions and design method for actual component selection.