Calculators

How to Calculate Percentage Increase & Decrease

Dev Nexus4 min read

Use one percentage change formula to handle increases, decreases, discounts and growth rates - with worked examples and the traps that catch people out.

"Prices are up undefined%." "That stock fell undefined%." "We grew undefined% year over year." Percentage change is the language of money, growth and comparison - but the moment you have to compute it yourself, the order of operations gets slippery.

This guide covers the single formula behind every increase and decrease, walks through worked examples for discounts and growth, and shows the mistakes that quietly produce wrong numbers.

The Problem

The mistake almost everyone makes is dividing by the wrong number. Percentage change is always measured against the original value, not the new one - and it is easy to mix them up when you are staring at two figures.

There is a second trap that feels counterintuitive: a rise and a fall of the same percent do not cancel out. Go up undefined% then down undefined% and you do not end up where you started. Get the base wrong and your discount, markup or growth figure is off - sometimes by a lot.

The Solution

One formula covers both directions: percentage change = (new − old) / old × 100. A positive result is an increase, a negative result is a decrease. That is it.

The key discipline is that old - the starting value - is always the denominator. From undefined to undefined, the change is (55 − 40) / 40 × 100 = 37.5%. From undefined back to undefined, it is (40 − 55) / 55 × 100 = −27.3%. Same two numbers, different bases, different answers. The Percentage Calculator applies this formula with the correct sign automatically, so you can check any figure in seconds without anything leaving your browser.

Step-by-Step Guide

1
Identify the old and new values
Decide which number is the starting point (old) and which is the result (new). For a price that went from $undefined to $undefined, old is undefined and new is undefined. Getting this straight up front prevents the most common error.
2
Subtract to find the difference
Compute new − old. For undefined to undefined, that is 55 − 40 = 15. If the result is negative, you already know you are dealing with a decrease - keep the minus sign, it carries meaning.
3
Divide by the original value
Divide the difference by the old value: 15 / 40 = 0.375. Always divide by the original, never the new figure. This is the step that decides whether your answer is right.
4
Multiply by 100 and read the sign
0.375 × 100 = 37.5%. A positive percentage is an increase, a negative one is a decrease. So $undefined to $undefined is a undefined.undefined% increase, and $undefined to $undefined is a undefined.undefined% decrease.
5
Reverse a discount when you need the original
To undo a discount, divide - do not add the percent back. A $undefined item after undefined% off came from 48 / (1 − 0.20) = 48 / 0.8 = $60. Multiplying $undefined by undefined.undefined gives $undefined.undefined, which is wrong.

Common Mistakes

Dividing by the new value
Percentage change is relative to where you started. Dividing by the new number instead of the original gives a different, incorrect figure - and it is the single most common percentage-change error.
Assuming an equal rise and fall cancel out
Up undefined% then down undefined% does not return you to the start. undefined rises to undefined, then a undefined% fall on undefined removes undefined, leaving undefined. The second percent is taken from a larger base, so the drop is bigger in absolute terms.
Confusing percentage points with percent change
An interest rate moving from undefined% to undefined% is a rise of undefined percentage points, but a undefined% increase. State which you mean - the two are wildly different when compounded or applied to money like a loan or EMI.
Adding the percent back to reverse a discount
Adding undefined% to a discounted price does not recover the original, because the undefined% was taken off a bigger number. Always divide the sale price by (undefined − discount) instead.

Frequently Asked Questions

What is the formula for percentage increase or decrease?

Use (new − old) / old × 100. A positive result is a percentage increase and a negative result is a percentage decrease. The old value is always the denominator.

How do I calculate a percentage increase?

Subtract the original from the new value, divide by the original, and multiply by 100. From 40 to 55: (55 − 40) / 40 × 100 = 37.5% increase.

How do I calculate a percentage decrease?

The same formula produces a negative result. From 55 to 40: (40 − 55) / 55 × 100 = −27.3%, meaning a 27.3% decrease.

Why don't an equal rise and fall cancel out?

Because each percent is taken from a different base. A 50% rise on 100 gives 150, but a 50% fall on 150 removes 75, leaving 75 - not the original 100.

How do I find the original price before a discount?

Divide the sale price by one minus the discount as a decimal. For $48 after 20% off: 48 / 0.8 = $60. Never simply add the percentage back to the discounted price.