Percentage error identifies the difference between the experimental values to its exact values. The simple per cent or percentage error formula** **helps calculate the error between the experimental measured value and an actual theoretical value. Such errors are mainly caused due to human or tool error like imprecision of equipment or adjustments issues.

## Per cent Error Formula

**Percentage Error=|E−T||T|×100**

E stands for the experimental value and T for the theoretical value in the per cent error formula. So, how to calculate percentage error? Let’s look at an example here:

Let’s say you are experimenting with measuring the boiling of water, and the average result is 101.5 °C. This is your experimental (E) value and water’s actual boiling point 100°C is the theoretical (T) value. What would be the per cent error between E and T?

Insert numbers into the per cent error formula.

|E−T||T|×100

=(101.5−100)|100|×100

=1.5100×100

=0.015×100

=1.5%

=1.5% error

## How To Calculate Percent Error?

Keep the following steps in mind while calculating the per cent error equation:

- When you subtract one value from another, you will likely get the ‘error’ value. In case you miss the sign, the order remains unchanged. But if you leave the subtraction sign, you get the ‘error’ by subtracting the theoretical value from the experimental value.
- Divide the ‘error’ value by the known value (not your theoretical value from the experimental value), giving you a decimal number.
- Next, multiply the decimal value with 100 to convert it to a % value.
- Add the % symbol to report the per cent error value.

Here are three examples of how to find per cent error using the percentage error formula:

**Example 1:**

Due to some marginal errors, your scale measures a wrong value as 8 cm. Let’s consider the scale’s actual measurement value is 12 cm. Calculate the percentage error using the per cent difference formula.

**Solution:**

Approximate value = 8 cm

Exact value = 12 cm

Percentage Error = (Approximate Value – Exact Value / Exact Value × 100)

Percentage Error = (8 – 12)/12 × 100

= -33.3%

**Example 2: **

In a rock concert, the organisers estimated 90 spectators. Instead, 120 people showed up at the concert. Calculate the per cent error using the formula.

**Solution:**

Approximate value = 90

Exact value = 120

The percent error formula= (Approximate Value – Exact Value / Exact Value × 100)

Percentage Error = (90– 120)/120 × 100

= 30/120 × 100 = 25%

**Example 3: **

Ole Rømer, a Danish astronomer, observed that despite the distance of Jupiter from Earth, the periods of Jupiter’s satellites fluctuated. The satellites were assumed to take a longer time to appear from the behind the Earth when Jupiter was further away. He gave an approximate value of 220,000 km/s for light velocity relative to the light speed. However, currently, the accepted value of the speed of light is 299,800 km/s. Solve the percentage error with the formula.

**Solution:**

Approximate value = 220,000 km/s = 2.2 x 108 m/s

Exact value = 299,800 km/s = 2.998 x 108 m/s

The percent error formula= (Approximate Value – Exact Value / Exact Value × 100)

Percentage Error = (2.2 x 108 m/s – 2.998 x 108 m/s)/ 2.998 x 108 m/s × 100

= 26.62%

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