Calculate a percentage
Use percent of a number, percentage change or percentage difference.
Choose the percentage question first
Start by choosing the type of percentage problem. Percent of a number asks for a part of a whole. Percentage change compares an old value with a new value. Percentage difference compares two values without treating either one as the starting point.
Enter the values in the fields that match the wording of the problem. This is more important than the arithmetic. Most wrong percentage answers come from choosing the wrong base value, not from multiplying or dividing incorrectly.
Reading percent, change, and difference
A percentage is a comparison to 100. The result only makes sense when you know what the 100 refers to. In a percent of a number problem, the whole is the base. In a change problem, the old value is the base. In a difference problem, the average of the two values is often used.
For change results, a positive answer means an increase. A negative answer means a decrease. For percent of a number, the result is the part represented by the selected percent.
The three percentage formulas
For percent of a number, use part = whole x percent / 100. For percentage change, use (new value - old value) / old value x 100. For percentage difference, use absolute difference / average of the two values x 100.
Those formulas answer different questions. Swapping them can give a number that looks precise but describes the wrong relationship. Always identify the base before trusting the result.
A percent-of-number example
If a price is 80 and you need 15 percent of it, calculate 80 x 15 / 100. The answer is 12. If the price moves from 80 to 92, the change is 12. Divide 12 by the old value, 80, then multiply by 100. The increase is 15 percent.
If you compare 80 and 92 as a percentage difference, the base is their average, 86. That gives about 13.95 percent. It is not the same question.
Where percentage problems go wrong
The most common mistake is using the new value as the denominator in a change problem. The old value is the reference point because the question asks how far the value moved from where it started.
Another mistake is adding percentage points and percent changes as if they were the same. Moving from 20 percent to 30 percent is a 10 percentage point increase, but it is a 50 percent relative increase.
Percentage Calculator FAQ
How do I calculate a percentage of a number?
Multiply the whole by the percent, then divide by 100. For example, 15 percent of 80 is 80 x 15 / 100, which equals 12.
The whole is the number the percentage is being taken from. If the problem says 15 percent of 80, 80 is the base.
What is the difference between percentage change and percentage difference?
Percentage change uses an old value and a new value. It shows increase or decrease from the old value. Percentage difference compares two values without direction, usually using their average as the base.
Use change for before and after situations. Use difference when the two values are side by side measurements or estimates.
Why does the old value matter in percentage change?
The old value is the starting point. A move from 50 to 65 is measured against 50 because that is where the change began. The formula is (65 - 50) / 50 x 100, which gives 30 percent.
If you divide by 65 instead, you answer a different question.
Can a percentage decrease be more than 100 percent?
For normal values that cannot go below zero, a decrease cannot be more than 100 percent. Dropping from 80 to 0 is a 100 percent decrease.
A calculated decrease below -100 percent usually means the values can cross zero, or the base and new value were entered in the wrong order.
Should I round the percentage result?
Round the final result to the precision the situation needs. For homework, follow the assignment rule. For shopping or everyday estimates, one or two decimal places is usually enough.
Avoid rounding halfway through a longer calculation. Early rounding can make the final percentage slightly wrong.