Percentages show up everywhere — discounts at checkout, salary raises, exam scores, price changes. The underlying formula is always the same, but people often get tripped up on which number is the “part” and which is the “whole,” especially when working backward from a percentage to find an original price.
The Core Formula
Percentage = (Part ÷ Whole) × 100
Example: if 25 out of 100 students passed an exam, that’s (25 ÷ 100) × 100 = 25%.
Percentage Increase
To find how much a value has increased in percentage terms:
Increase % = [(New Value − Old Value) ÷ Old Value] × 100
Example: a price goes from $80 to $100. Increase = [(100 − 80) ÷ 80] × 100 = 25%.
Percentage Decrease (and Discounts)
Same formula, just with the values reversed, since the new value is lower:
Decrease % = [(Old Value − New Value) ÷ Old Value] × 100
For a discount, if you already know the percentage off, the final price is: Original Price × (1 − Discount%). A $100 item at 20% off costs $100 × 0.8 = $80.
Working Backward: Finding the Original Value
This is where most manual mistakes happen. If a discounted price is $80 after a 20% discount, the original price is NOT $80 + 20% of $80. It’s:
Original = Discounted Price ÷ (1 − Discount%) = 80 ÷ 0.8 = $100
Calculate It Instantly
The Nest Tools’ Percentage Calculator covers all of these cases — basic percentage, increase/decrease, discounts, and reverse percentage — without needing to remember which formula applies to which situation.
If you are stacking multiple discounts, like a sale price plus a coupon, our Discount Calculator handles that directly and shows your true effective discount rate, since stacked discounts do not simply add together.
Frequently Asked Questions
Is a 20% increase followed by a 20% decrease back to the original value?
No. Because the second percentage is calculated on a different (larger) base, you end up slightly below the original value.
What’s the difference between percentage change and percentage points?
If a rate goes from 10% to 15%, that’s a 5 percentage point increase, but a 50% relative increase (5 ÷ 10 × 100). The two are often confused.