Length of Belt Calculator

✖Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley.ⓘ Centre Distance between Pulleys [C]			+10% -10%
✖Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.ⓘ Diameter of Big Pulley [D]			+10% -10%
✖Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.ⓘ Diameter of Small Pulley [d]			+10% -10%

✖Belt Length is the length of the transmission belt that is used to transmit power from one pulley to the other.ⓘ Length of Belt [L]

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Formula

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Length of Belt

Formula

L = (2 \cdot C) + (π \cdot \frac{D + d}{2}) + (\frac{{(D - d)}^{2}}{4 \cdot C})

Example

4942.023 mm = (2 \cdot 1600 mm) + (π \cdot \frac{810 mm + 270 mm}{2}) + (\frac{{(810 mm - 270 mm)}^{2}}{4 \cdot 1600 mm})

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Length of Belt Solution

STEP 0: Pre-Calculation Summary

Formula Used

Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys))
L = (2*C)+(pi*(D+d)/2)+(((D-d)^2)/(4*C))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Belt Length - (Measured in Meter) - Belt Length is the length of the transmission belt that is used to transmit power from one pulley to the other.
Centre Distance between Pulleys - (Measured in Meter) - Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley.
Diameter of Big Pulley - (Measured in Meter) - Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.
Diameter of Small Pulley - (Measured in Meter) - Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.

STEP 1: Convert Input(s) to Base Unit

Centre Distance between Pulleys: 1600 Millimeter --> 1.6 Meter (Check conversion here)
Diameter of Big Pulley: 810 Millimeter --> 0.81 Meter (Check conversion here)
Diameter of Small Pulley: 270 Millimeter --> 0.27 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (2*C)+(pi*(D+d)/2)+(((D-d)^2)/(4*C)) --> (2*1.6)+(pi*(0.81+0.27)/2)+(((0.81-0.27)^2)/(4*1.6))

Evaluating ... ...

L = 4.94202253293849

STEP 3: Convert Result to Output's Unit

4.94202253293849 Meter -->4942.02253293849 Millimeter (Check conversion here)

FINAL ANSWER

4942.02253293849 ≈ 4942.023 Millimeter <-- Belt Length

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Belt Drives » Introduction of Belt Drives » Length of Belt

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Introduction of Belt Drives Calculators

Wrap Angle for Small Pulley

Go Wrap Angle on Small Pulley = 3.14-(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Small Pulley given Wrap Angle of Small Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Big Pulley given Wrap Angle of Small Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Length of Belt Formula

Define Wrap Angle?

The wrap angle is defined as the angle between the run-up and run-off of the belt on the pulley. In addition, the greater curvature causes greater bending stresses in the belt, which also limits the transmittable belt force. So-called idler pulleys can be used to increase the wrap angle.

How to Calculate Length of Belt?

Length of Belt calculator uses Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys)) to calculate the Belt Length, The length of Belt formula is defined as the pitch length and is measured at the pitch diameter of the sheaves. Both effective length and pitch length are measured with the belt tensioned by a specified amount. Belt Length is denoted by L symbol.

How to calculate Length of Belt using this online calculator? To use this online calculator for Length of Belt, enter Centre Distance between Pulleys (C), Diameter of Big Pulley (D) & Diameter of Small Pulley (d) and hit the calculate button. Here is how the Length of Belt calculation can be explained with given input values -> 4.9E+6 = (2*1.6)+(pi*(0.81+0.27)/2)+(((0.81-0.27)^2)/(4*1.6)).

FAQ

What is Length of Belt?

The length of Belt formula is defined as the pitch length and is measured at the pitch diameter of the sheaves. Both effective length and pitch length are measured with the belt tensioned by a specified amount and is represented as L = (2*C)+(pi*(D+d)/2)+(((D-d)^2)/(4*C)) or Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys)). Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley, Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley & Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.

How to calculate Length of Belt?

The length of Belt formula is defined as the pitch length and is measured at the pitch diameter of the sheaves. Both effective length and pitch length are measured with the belt tensioned by a specified amount is calculated using Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys)). To calculate Length of Belt, you need Centre Distance between Pulleys (C), Diameter of Big Pulley (D) & Diameter of Small Pulley (d). With our tool, you need to enter the respective value for Centre Distance between Pulleys, Diameter of Big Pulley & Diameter of Small Pulley and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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