Belt Length Calculator is a free online tool that computes the belt length be it ribbed, flat, timing or v-belt. All you need to do is enter the input parameters like large pulley diamter, small pulley diamter, centre distance and tap on the calculate button to find the belt length in no time.

**Belt Length Calculator: **If you are worried on how to find the length of a belt be it
timing, v or flat type you are on the right destination that sets you tension free. Get acquainted with
belt length formula and step by step process for determining the belt length along with derivation.
Learn how to calculate length of a belt in two pulley system with varying parameters of pulleys.

Follow the below mentiond steps to evaluate the belt length and get the result easily. They are in the following fashion./p>

- Firstly, evaluate the dimater of large, small pulleys, distance between pulley axles.
- Later, compute the sum and difference between pulleys, square of distance between pulley axles
- Substitute the values found in the Belt Length Formula and determine the belt length.

Know how to calculate the belt length by using the below listed formula for belt length in a two pulley system. Substitute the diamters of the pulleys and distance between the axles and find out the belt length.

Belt Length = ((D_{L}+D_{S})*π/2)
+(D_{L}-D_{S})*arcsin((D_{L}-D_{S})/2L)+2*sqrt(L^{2}-0.25*(D_{L}-D_{S})^{2})

Where D_{L} means diamter of the large pulley

D_{S} means diamter of the smaller pulley

L stands for distance between pulley axles

**Example**

**Question: Compute the belt length of a two pulley system if the diameters of the large pulley is
25m and smaller pulley is 15m and Distance between the pulley axles is 21m?**

**Solution:**

Given that

Diamter of Larger Pulley D_{L} = 25 m

Diamter of the Smaller Pulley D_{S} = 15 m

Pulley Centre Distance L = 21 m

We know the formula to find the belt length is given by Belt Length =
((D_{L}+D_{S})*π/2)
+(D_{L}-D_{S})*arcsin((D_{L}-D_{S})/2L)+2*sqrt(L^{2}-0.25*(D_{L}-D_{S})^{2})

Input the values in the formula as long as all the metrics are in same units or else change them all into similar units.

Substitute the input values in the belt length formula and we have the equation as follows

Belt Length = ((25+15)*π/2) +(25-15)*arcsin((25-15)/2*21)+2*sqrt(21^{2}-0.25*(25-15)^{2})

Simplifying the equation further we have

=106.03m

Physicscalc.Com has got concepts related to classical mechanics, rotational and periodic motion, waves, optics, fluid mechanics, friction, and many more along with their relevant calculators all one under one roof.

If you don't have time and can go for an approximate calculation of belt length you can use this alternative formula and find out the belt length easily.

Belt Length = ((D_{L}+D_{S})*π/2) +(2*L)+(D_{L}-D_{S})^{2}/(4*L)

Where D_{L} means diamter of the large pulley

D_{S} means diamter of the smaller pulley

L stands for distance between pulley axles

You can use this simplified formula when you want to make faster calculations. However, this formula fails if one pulley is larger than the other or both of them are closer together.

**1. What is meant by Belt Length?**

Belt Length is the length spread out between two pulleys in which the pulleys are of unequal radii.

**2. What does D _{L} and D_{S} stand for in the Belt Length
Formula?**

D_{L} and D_{S} are nothing but the diamters of the larger pulley and the
smaller pulley.

**3. What is the formula to determine the Belt Length?**

The Formula for Belt Length is given by Belt Length = ((D_{L}+D_{S})*π/2)
+(D_{L}-D_{S})*arcsin((D_{L}-D_{S})/2L)+2*sqrt(L^{2}-0.25*(D_{L}-D_{S})^{2})