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Percent Change Calculator
Calculate percent change from an old value to a new one, the percent difference between two values, or an average rate of change.
The starting value. Percent change divides by this number.
The value after the change.
Enter an old value and a new value to see the percent change.
This percent change calculator is for classwork that asks how a value moved. Enter an old value and a new value to see an increase or a decrease: new minus old, divided by the absolute value of the old value, times 100. A second mode finds the percent difference, the absolute gap divided by the average of the absolute values. A third mode finds the average rate of change between two points and shows the fraction and the decimal. A change from zero, or two x-values that match, is explained as undefined instead of infinity.
Percent change from an old value to a new value
Percent change asks how a new value compares with an old one. Subtract the old value from the new value, divide by the absolute value of the old value, and multiply by 100. A positive result is an increase. A negative result is a decrease. The absolute value in the denominator matters when the starting number is negative: without it, a value that went up can look like a decrease.
From 50 to 75, (75 − 50) / 50 = 1/2 = 50%, a 50% increase. From 80 to 60, (60 − 80) / 80 = −1/4, a 25% decrease. From −20 to −10 the value went up, and (−10 − (−20)) / |−20| = 1/2, a 50% increase. If the old value is 0, percent change is undefined, because the formula would divide by zero. The page says that in a sentence. It does not show infinity. When a decimal runs on, the display keeps 8 significant figures and says that it is rounded.
Percent difference, when neither value is the start
Percent difference compares two numbers when neither one is the original. Order does not matter, and the result is not an increase or a decrease. Divide the absolute gap by the average of the absolute values, then multiply by 100: |a − b| / ((|a| + |b|) / 2) × 100. For 50 and 75, |50 − 75| / ((50 + 75) / 2) = 2/5 = 40%.
Classroom pages usually write that denominator as the average of the signed values, (a + b) / 2, and they state it for positive numbers. For positive numbers the two averages are the same, so 50 and 75 is 40% either way. The absolute values keep the same comparison defined when a value is negative, and they keep the percentage from flipping sign. If both values are 0, there is no difference to compare.
Average rate of change between two points
The average rate of change from one point to another is how much y changes for each unit x changes: (y₂ − y₁) / (x₂ − x₁). It is a rate. From (1, 2) to (3, 6), (6 − 2) / (3 − 1) = 2/1 = 2, so the rate is 2. The page shows that fraction and the matching decimal. Whole-number inputs are reduced before the decimal is written. If x₂ equals x₁, the rate is undefined, because the denominator is zero.
A different percent question
Frequently Asked Questions
What is the percent change formula?
Percent change = (new − old) / |old| × 100. From 50 to 75 that is (75 − 50) / 50 = 1/2 = 50%, an increase. From 80 to 60 it is a 25% decrease. From −20 to −10 it is a 50% increase, because the value went up. A long decimal is rounded to 8 significant figures.
What is the percent difference formula?
Percent difference = |a − b| / ((|a| + |b|) / 2) × 100. The denominator is the average of the absolute values. For 50 and 75 that is |50 − 75| / ((50 + 75) / 2) = 2/5 = 40%. School pages often divide by the average of the signed values, (a + b) / 2. Those two averages match when both numbers are positive.
How is percent change different from percent difference?
Percent change needs an old value and a new value, keeps a direction, and divides by the old value. Percent difference has no direction, so swapping the numbers does not change it, and it divides by an average. A move from 80 to 60 is a 25% decrease. The percent difference between 80 and 60 is a different question.
What is the average rate of change?
Average rate of change = (y₂ − y₁) / (x₂ − x₁). From (1, 2) to (3, 6) the fraction is 2/1 and the decimal is 2. If x₂ equals x₁, the rate is undefined. This is a rate between two points, not a percent.
Why is percent change undefined when the old value is 0?
The formula divides by the old value. Division by zero has no result, so a change from 0 to 5 is undefined. The calculator says so in words and does not show infinity. Percent difference is separate: if both values are 0, there is no difference to compare.