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Length of Belt Formula

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Belt Length is the length of the transmission belt that is used to transmit power from one pulley to the other. Check FAQs

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

L - Belt Length?C - Centre Distance between Pulleys?D - Diameter of Big Pulley?d - Diameter of Small Pulley?π - Archimedes' constant?

Length of Belt Example

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Here is how the Length of Belt equation looks like with Values.

Here is how the Length of Belt equation looks like with Units.

Here is how the Length of Belt equation looks like.

4942.0225 = (2 \cdot 1600) + (3.1416 \cdot \frac{810 + 270}{2}) + (\frac{{(810 - 270)}^{2}}{4 \cdot 1600})

4942.0225mm = (2 \cdot 1600mm) + (3.1416 \cdot \frac{810mm + 270mm}{2}) + (\frac{{(810mm - 270mm)}^{2}}{4 \cdot 1600mm})

4942.0225 = (2 \cdot 1600) + (3.1416 \cdot \frac{810 + 270}{2}) + (\frac{{(810 - 270)}^{2}}{4 \cdot 1600})

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Length of Belt Solution

Follow our step by step solution on how to calculate Length of Belt?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

L = (2 \cdot 1600mm) + (3.1416 \cdot \frac{810mm + 270mm}{2}) + (\frac{{(810mm - 270mm)}^{2}}{4 \cdot 1600mm})

Next Step Convert Units

∴

L = (2 \cdot 1.6m) + (3.1416 \cdot \frac{0.81m + 0.27m}{2}) + (\frac{{(0.81m - 0.27m)}^{2}}{4 \cdot 1.6m})

Next Step Prepare to Evaluate

∴

L = (2 \cdot 1.6) + (3.1416 \cdot \frac{0.81 + 0.27}{2}) + (\frac{{(0.81 - 0.27)}^{2}}{4 \cdot 1.6})

Next Step Evaluate

∴

L = 4.94202253293849m

Next Step Convert to Output's Unit

∴

L = 4942.02253293849mm

LAST Step Rounding Answer

∴

L = 4942.0225mm

Length of Belt Formula Elements

Variables

Constants

Belt Length

Belt Length is the length of the transmission belt that is used to transmit power from one pulley to the other.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Belt Length

Centre Distance between Pulleys

Centre Distance between Pulleys is the distance between the centres of the big pulley and the small pulley.

Symbol: C

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Centre Distance between Pulleys

Diameter of Big Pulley

Diameter of Big Pulley is the distance from side to side of the flat of the Big pulley.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Big Pulley

Diameter of Small Pulley

Diameter of Small Pulley is the distance from side to side of the flat of the Small pulley.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Small Pulley

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Introduction of Belt Drives category

Go Wrap Angle for Small Pulley

α s = 3.14 - (2 \cdot (a \sin (\frac{D - d}{2 \cdot C})))

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

C = \frac{D - d}{2 \cdot \sin (\frac{3.14 - α s}{2})}

Go Diameter of Small Pulley given Wrap Angle of Small Pulley

d = D - (2 \cdot C \cdot \sin (\frac{3.14 - α s}{2}))

Go Diameter of Big Pulley given Wrap Angle of Small Pulley

D = d + (2 \cdot C \cdot \sin (\frac{3.14 - α s}{2}))

How to Evaluate Length of Belt?

Length of Belt evaluator 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 evaluate 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 evaluate Length of Belt using this online evaluator? To use this online evaluator 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.

FAQs on Length of Belt

What is the formula to find Length of Belt?

The formula of Length of Belt is expressed as 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)). Here is an example- 4.9E+6 = (2*1.6)+(pi*(0.81+0.27)/2)+(((0.81-0.27)^2)/(4*1.6)).

How to calculate Length of Belt?

With Centre Distance between Pulleys (C), Diameter of Big Pulley (D) & Diameter of Small Pulley (d) we can find Length of Belt using the formula - 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)). This formula also uses Archimedes' constant .

Can the Length of Belt be negative?

No, the Length of Belt, measured in Length cannot be negative.

Which unit is used to measure Length of Belt?

Length of Belt is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Belt can be measured.

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Length of Belt Formula

Length of Belt Example

Length of Belt Solution

Length of Belt Formula Elements

Other formulas in Introduction of Belt Drives category

How to Evaluate Length of Belt?

FAQs on Length of Belt

Variable Name