# Percent Error Formula

**Percent Error** calculates the percentage difference between actual value and measured value. It tells us how close the measured value is to be true. There may be slight manufacturing errors for the instruments that are used for measurements and can never be assumed to be exact. For this kind of problem percent error helps us to specify to what extent it will be true. The formula for this percent error is given by

Percent Error = (|Measured Value – Actual Value|/Actual Value) × 100

To get more understanding from the formula, let’s look into a few examples

**Question 1: The actual length of a straight line is 8cm and when we measured with a scale it was 7cm (Wrong value) due to some marginal error. What is the percentage error?**

**Solution:**

Given,

Measured value = 7cm

Actual Value = 8cm

Percent error = (|Measured Value-Actual Value| / Actual Value) x 100

= (|7-8| / 8) x 100

= (|-1| / 8) x 100

= (1/8) x 100

= 12.5%

So percentage error is 12.5%

**Question 2: What is the percentage error if the measured value is 40cm and the** **Actual value is 50cm?**

**Solution:**

Given,

Measured value=40cm

Actual Value=50cm

Percent error = (|Measured Value-Actual Value| / Actual Value) x 100

= (|40-50| / 50) x 100

= (|-10| / 50) x 100

= (10/50) x 100

= 20%

So percentage error is 20%

**Question 3: A scale measures wrongly a value as 15 cm due to some marginal errors. Find the percentage error if the actual measurement of the value is 14 cm.**

**Solution:**

Given,

Measured value=15cm

Actual Value=14cm

Percent error= ( |Measured Value-Actual Value| / Actual Value ) x 100

= ( |15-14| / 14 ) x 100

= ( |1| / 14 ) x 100

= 100/14

= 7.14%

So percentage error is 7.14%

**Question 4: What is the percentage error if the measured value is 11cm and the** **Actual value is 10cm?**

**Solution:**

Given,

Measured value=11cm (wrongly measured)

Actual Value=10cm (Exact value)

Percent error= ( |Measured Value-Actual Value| / Actual Value ) x 100

= ( |11-10| / 10 ) x 100

= ( |1| / 10 ) x 100

= 100/10

= 10%

So percentage error is 10%

**Question 5: Find the percentage error if the wrongly measured value is 100cm and the** **Actual value is 105cm?**

**Solution:**

Given,

Wrongly Measured value=100cm

Actual Value=105cm

Percent error= (|Measured Value-Actual Value| / Actual Value) x 100

= (|100-105| / 105) x 100

= (|-5| / 105) x 100

= (5/105) x 100

= 100/21

= 4.76%

So percentage error for the above data is 4.76%