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Calcimator

Belt Drive Design Calculator

Design V-belt or flat belt drives. Calculate belt length, speed ratio, belt speed, and tight/slack side tensions for power transmission.

About this calculator

A belt drive transmits rotational power between two shafts using pulleys of different sizes and a belt running between them. This calculator sizes an open (non-crossed) belt drive from the two pulley diameters, the shaft center distance, the driver's operating speed, and the horsepower being transmitted. The Speed Ratio (Driven Diameter / Driver Diameter) tells you how much the output shaft slows down and gains torque relative to the input -- a driven pulley twice the driver's diameter halves output speed and roughly doubles output torque, assuming no belt slip. Belt Length uses the standard open-belt approximation, L = 2C + pi(D+d)/2 + (D-d)^2/(4C), which is accurate for the shallow wrap angles typical of ordinary two-pulley drives; order the nearest standard belt length once you have a result, since belts aren't cut to arbitrary lengths.

Belt Speed follows directly from the driver pulley's diameter and RPM, and matters because most V-belt cross-sections have a maximum rated speed beyond which centrifugal effects reduce the belt's usable pull. Tight Side and Slack Side Tension come from the capstan (belt-friction) relationship T1/T2 = e^(mu x theta), using the wrap angle on the smaller pulley and an assumed friction coefficient typical of a V-belt in reasonable condition -- these tensions size the shaft bearings and confirm the belt itself isn't overloaded. Treat the tension outputs as an estimate: real friction depends on belt condition, groove wear, and installed tension, so a bearing or belt selected right at the calculated limit leaves no margin for those variables.

Inputs

in
in
in
RPM
HP

Results

Speed Ratio

2:1

Belt Length

76.65 in

≈ 13 smartphones

Belt Speed2,749 ft/min
Tight Side Tension94.3 lb
Slack Side Tension34.3 lb
How to Use This Calculator
  1. Enter the Driver Pulley Diameter in inches — use the pitch diameter for V-belts, not the outside diameter.
  2. Enter the Driven Pulley Diameter. A larger driven pulley reduces output speed and increases torque (speed reduction).
  3. Set the Center Distance between shaft centerlines in inches. Aim for 1–2× the sum of the pulley diameters for good wrap angle.
  4. Enter the Motor Speed in RPM and the Transmitted Horsepower for the application.
  5. Review the Speed Ratio and Belt Length — use the belt length to order the correct standard V-belt designation.
  6. Check Tight Side and Slack Side Tensions to verify the shaft bearings and belt are rated for those loads.

How the result changes with Driver Pulley Diameter

Driver Pulley DiameterSpeed RatioBelt Length
34:172.41 in
4.52.67:174.5 in
91.33:181.08 in
150.8:190.51 in

What each input means

Driver Pulley Diameter
Effective diameter of the driving (motor) pulley. For V-belts, use the pitch diameter.
Driven Pulley Diameter
Effective diameter of the driven (load) pulley. Larger gives more speed reduction.
Center Distance
Distance between pulley shaft centers. Should be 1-2× the sum of pulley diameters for good wrap angle.
Motor Speed
Speed of the driver pulley (motor). Common motor speeds: 1150, 1750, 3500 RPM.
Transmitted Horsepower
Power to be transmitted through the belt drive system.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    5 parameters
    Driver Pulley Diameter = 6, Driven Pulley Diameter = 12, Center Distance = 24, Motor Speed = 1750, Transmitted Horsepower = 5 = 5 input(s) provided
  2. Calculate Speed Ratio
    Speed Ratio
    2 = 2
  3. Calculate Belt Length
    Belt Length
    76.65 = 76.65
  4. Calculate Belt Speed
    Belt Speed
    2749 = 2749
  5. Calculate Tight Side Tension
    Tight Side Tension
    94.3 = 94.3

Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does a larger driven pulley reduce output speed?

The Speed Ratio is the driven pulley's diameter divided by the driver's, and for a belt running at a fixed linear speed, a larger-diameter pulley must rotate more slowly to keep that belt speed constant -- the same reason a bicycle's larger rear sprocket turns the wheel more slowly per pedal stroke than a smaller one. Raising the Driven Pulley Diameter therefore raises the Speed Ratio and lowers output shaft speed, while raising the Driver Pulley Diameter does the opposite.

What happens to belt tension when I increase the transmitted horsepower?

Both the Tight Side and Slack Side Tension rise as Transmitted Horsepower goes up, because the effective pull the belt must deliver (and therefore the difference between the two tensions) scales directly with the power being transmitted at a given belt speed. Higher horsepower at the same speed always means a belt working harder, which is why a drive redesigned for more power usually needs a wider belt, an additional belt in parallel, or a shorter center distance to raise the wrap angle.

Does running the drive faster reduce the belt tension for the same horsepower?

Yes. For a fixed Transmitted Horsepower, the effective pull the belt must carry is inversely proportional to belt speed, so raising the Motor Speed (which raises belt speed for a given driver pulley) lowers both the Tight Side and Slack Side Tension. This is the same reason high-speed power transmission favors smaller belts and pulleys -- moving the same power at higher speed requires less force.

Why doesn't Transmitted Horsepower change the Belt Length or Speed Ratio?

Belt Length and Speed Ratio are purely geometric -- they depend only on the two pulley diameters and the center distance between shafts. Horsepower affects how hard the belt and bearings work (through the tension outputs), not the physical layout of the drive, so changing it leaves Belt Length and Speed Ratio exactly where they were.

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