V-Belt & Timing Pulley Pitch Length, Speed Ratio & Driven RPM Calculator

Size belt length L = 2C + π(D+d)/2 + (D−d)²/(4C) and driven pulley speed.

Total Belt Pitch Length
54.35 in
Driven Pulley Output Speed 765.63 RPM
Speed Reduction Ratio (D : d) 2.29 : 1
Belt Linear Surface Speed 1,603.52 ft/min
Inputs
in
Motor drive pulley pitch diameter (d) in inches.
in
Driven machine pulley pitch diameter (D) in inches.
in
Shaft center-to-center distance (C) in inches.
RPM
Drive motor rotational speed in RPM.
Results & Graph
Total Belt Pitch Length
54.35 in
Driven Pulley Output Speed
765.63 RPM
Speed Reduction Ratio (D : d)
2.29 : 1
Belt Linear Surface Speed
1,603.52 ft/min

Total Belt Pitch Length

Graph 1 • Drive Pulley Dia In Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 in 30.7 in 61.5 in 50%: 51.86 in 51.9 50% 75%: 53.09 in 53.1 75% 100%: 54.35 in 54.4 100% 125%: 55.62 in 55.6 125% 150%: 56.92 in 56.9 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Total Belt Pitch Length 54.35 in Driven Pulley Output Speed 765.63 RPM Speed Reduction Ratio (D : d) 2.29 : 1 Belt Linear Surface Speed 1,603.52 ft/min
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Total Belt Pitch Length54.35 inDriven Pulley Output Speed765.63 RPMSpeed Reduction Ratio (D : d)2.29 : 1Belt Linear Surface Speed1,603.52 ft/min
Summary: With 3.5" drive and 8" driven sheaves at 18" centers, belt pitch length is 54.35" and driven shaft speed is 766 RPM.
Summary: With 3.5" drive and 8" driven sheaves at 18" centers, belt pitch length is 54.35" and driven shaft speed is 766 RPM.
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Formula & Mathematical Methodology: Belt & Pulley Length Formula

BeltLength = 2·C + 1.5708·(D + d) + (D − d)² / (4·C)
DrivenRPM = MotorRPM × (d / D)
BeltLength = 2·C + 1.5708·(D + d) + (D − d)² / (4·C); DrivenRPM = MotorRPM × (d / D)
  • drivePulleyDiaIn: Drive Pulley Dia In (in)
  • drivenPulleyDiaIn: Driven Pulley Dia In (in)
  • centerDistanceIn: Center Distance In (in)
  • motorSpeedRpm: Motor Speed Rpm (RPM)

Rounding: Physical package counts round up where appropriate; continuous measurements round to 2 decimal places.

Worked Example: Practical Benchmark: Belt & Pulley Length

Size belt length L = 2C + π(D+d)/2 + (D−d)²/(4C) and driven pulley speed.

  1. Enter your project dimensions, machining speeds, or recipe weights.
  2. Compute the governing equation: BeltLength = 2·C + 1.5708·(D + d) + (D − d)² / (4·C); DrivenRPM = MotorRPM × (d / D).
  3. Review the primary result, supporting dimensions, and 3 SVG visualizations.
Result: Computes Belt & Pulley Length via BeltLength = 2·C + 1.5708·(D + d) + (D − d)² / (4·C); DrivenRPM = MotorRPM × (d / D).

Frequently Asked Questions

How does the V-Belt & Timing Pulley Pitch Length, Speed Ratio & Driven RPM Calculator calculate results?

It evaluates BeltLength = 2·C + 1.5708·(D + d) + (D − d)² / (4·C); DrivenRPM = MotorRPM × (d / D) directly in your browser and plots three custom SVG visualizations.

Can I compare different material dimensions or batch sizes side by side?

Yes. Click "Compare (0/3)" in the results toolbar to pin up to 3 scenarios side by side.

Can I print a clean shop or kitchen reference sheet?

Yes. Click the Print button in the results toolbar for a distraction-free worksheet.

Science & Engineering · Mechanical & Shop Engineering

V-Belt & Timing Pulley Pitch Length, Speed Ratio & Driven RPM Calculator: inputs, method, and how to read the result

Size belt length L = 2C + π(D+d)/2 + (D−d)²/(4C) and driven pulley speed.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Drive Pulley Dia In: Motor drive pulley pitch diameter (d) in inches.
  • Driven Pulley Dia In: Driven machine pulley pitch diameter (D) in inches.
  • Center Distance In: Shaft center-to-center distance (C) in inches.
  • Motor Speed Rpm: Drive motor rotational speed in RPM.

What the calculation includes

With the default values shown, Total Belt Pitch Length is 54.35 in. The calculation follows Belt & Pulley Length Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Drive Pulley Dia In from 3.5 in to 3.85 in changes Total Belt Pitch Length from 54.35 in to 54.85 in. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard North American & metric trade dimensions, Machinery’s Handbook formulas, and culinary weight ratios.
  • Verify local municipal building codes, tool manufacturer limits, and food-safety time/temperature tables before execution.

Scope: Trade, Shop & Culinary Science Reference Standard Check the assumptions and limitations against your situation before relying on the estimate.

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