Calculators

Algebra

Percent Calculators

Enter a value and a percent tolerance to find the upper and lower limits of the tolerance range.

Input whole numbers or decimal numbers in the calculator. Enter the tolerance as a percentage without the ± sign. So for a tolerance of ±5% enter 5.

What is Percent Tolerance?

Tolerance is a measure used in manufacturing, engineering and quality control settings. Percent tolerance is the percentage a value may vary and still remain within acceptable limits. A tolerance of ±5% for example, means the measured value can be up to 5% more or 5% less than the target value to remain within tolerance.

For example, say a bag of jelly beans has a label weight of 16 ounces with a tolerance of ±2%. 2% of 16 ounces is 0.32 ounces. The bag can weigh as little as 15.68 ounces or as much as 16.32 ounces and still be within acceptable limits of tolerance.

Try the calculation: 16 ounces with a tolerance of ± 2%

How to Calculate Percent Tolerance

1. Divide the percent tolerance by 100 to get a decimal
2. Multiply the value by that decimal to get the tolerance amount
3. Add the tolerance amount to the value to get the upper limit
4. Subtract the tolerance amount from the value to get the lower limit

Example Problem: Percent Tolerance

A resistor is rated at 220 ohms with a tolerance of ±5%. What are the lowest and highest resistance values that are within tolerance?

Divide the percent tolerance by 100.

5 / 100 = 0.05

Multiply the value by 0.05 to get the tolerance amount.

220 × 0.05 = 11

Add and subtract the tolerance amount from the named rating value.

220 + 11 = 231
220 - 11 = 209

So a 220 ohm resistor with a 5% tolerance can measure anywhere from 209 to 231 ohms of resistance.

Percent Tolerance Formula

Where V is the value and T is the percent tolerance:

\[ \text{Upper Limit} = V + \lvert V \rvert \dfrac{T}{100} \] \[ \text{Lower Limit} = V - \lvert V \rvert \dfrac{T}{100} \]

These work for a negative value too. For a positive value they are the same as

\[ \text{Limits} = V \left( 1 \pm \dfrac{T}{100} \right) \]

You may notice that this is the same formula used to find the experimental value in our Percent Error Calculator. A measured value is within tolerance when its percent error, compared to the stated value, is less than or equal to the percent tolerance.

Other CalculatorSoup^® Percentage Calculators

Use the Percent Error Calculator to find how far a measured value is from the expected value as a percentage.

Use the Percentage Increase Calculator or the Percentage Decrease Calculator to find the percent increase or decrease from one value to another.

The Percent Change Calculator finds the change between two numbers as a percentage.