# Efficiency Formula

The efficiency of an object is defined as the ability to get close to a certain output from a given input with the least amount of waste. It can be interpreted as the amount of labor or energy saved in a process. Mathematically, it is the ratio of work accomplished by a machine or process to total energy expended or heat consumed. It is denoted by the symbol eta (η). Its formula equals the ratio of output work to input work multiplied by 100. Its unit of measurement is a percentage (%).

### Efficiency Formula

η = (W_{o}/W_{i}) × 100Where,

- η is the percentage efficiency,
- W
_{o}is the output work,- W
_{i}is the input work.

In terms of input energy and output energy, the formula is given as,

η = (E_{o}/E_{i}) × 100Where,

- η is the percentage efficiency,
- E
_{o}is the output work,- E
_{i}is the input work.

### Sample Problems

**Problem 1: Calculate the efficiency of a machine if input energy is 200 J and output energy is 150 J.**

**Solution:**

We have,

E

_{o}= 150E

_{i}= 200Using the formula we have,

η = (E

_{o}/E_{i}) × 100= (150/200) × 100

= 75%

**Problem 2: Calculate the efficiency of a machine if input energy is 450 J and output energy is 300 J.**

**Solution:**

We have,

E

_{o}= 300E

_{i}= 450Using the formula we have,

η = (E

_{o}/E_{i}) × 100= (300/450) × 100

= 66.67%

**Problem 3: Calculate the efficiency of a motor engine if 500 J work is done to give an output work of 100 J.**

**Solution:**

We have,

W

_{o}= 100W

_{i}= 500Using the formula we have,

η = (W

_{o}/W_{i}) × 100= (100/500) × 100

= 20%

**Problem 4: Calculate the output energy if the efficiency of a machine is 52% and the input energy is 250 J.**

**Solution:**

We have,

η = 52%

E

_{i}= 250Using the formula we have,

η = (E

_{o}/E_{i}) × 100=> E

_{o}= nE_{i}/100= 52 (250)/100

= 130 J

**Problem 5: Calculate the output energy if the efficiency of a machine is 72% and the input energy is 420 J.**

**Solution:**

We have,

η = 72%

E

_{i}= 420Using the formula we have,

η = (E

_{o}/E_{i}) × 100=> E

_{o}= nE_{i}/100= 72 (420)/100

= 302.4 J

**Problem 6: Calculate the input energy if the efficiency of a machine is 45% and the output energy is 300 J.**

**Solution:**

We have,

η = 45%

E

_{o}= 300Using the formula we have,

η = (E

_{o}/E_{i}) × 100=> E

_{i}= (E_{o}/n) × 100= (300/45) × 100

= 666.67 J

**Problem 7: Calculate the input energy if the efficiency of a machine is 56% and the output energy is 600 J.**

**Solution:**

We have,

η = 56%

E

_{o}= 600Using the formula we have,

η = (E

_{o}/E_{i}) × 100=> E

_{i}= (E_{o}/n) × 100= (600/56) × 100

= 1071.42 J