MATHEMATICAL GUIDE

Reverse Percentage Explained

Learn how to work backward from a known percentage portion to find the original whole number before discounts, markups, or taxes were applied.

Reverse Multiplier

Invert the decimal multiplier to work backward to the starting total.

Pre-Tax Totals

Extract original pre-tax amounts from sales tax or VAT receipts.

Discount Reversals

Determine the original retail price from a discounted purchase price.

1. The Reverse Percentage Formula

When you know what fraction of a total a number represents, you can recover the original whole by dividing by the decimal rate:

Whole = Part ÷ (Percentage ÷ 100)

For example, if 30 is 20% of a number: Whole = 30 ÷ (20 ÷ 100) = 30 ÷ 0.20 = 150.

2. Reverse Percentages with Increases & Decreases

If an amount was increased by P%, the final value represents (100 + P)% of the base. If it was decreased, it represents (100 − P)%:

Original (after increase) = Final Value ÷ (1 + P/100)
Original (after discount) = Final Value ÷ (1 − P/100)

3. Interactive Calculator

Use our Percentage Calculator in Mode C (“X is P% of what?”) to calculate reverse percentages instantly:

Open Percentage Calculator

Frequently Asked Questions

What is a reverse percentage calculation?

A reverse percentage calculation finds the original whole number before a percentage was calculated, added, or subtracted. It answers questions like: 'If $30 is 20% of a number, what was the full number?'

Why can't I just add the discount percentage back to the sale price?

Because the percentage discount was taken from the original, larger base. For example, if a $100 jacket is discounted by 20%, the sale price is $80. Adding 20% to $80 gives only $96 ($80 + $16), not the original $100. To find the original, divide by (1 − 0.20): $80 ÷ 0.80 = $100.

How do I calculate pre-tax price from a total with sales tax?

Divide the total price by (1 + tax rate as decimal). For example, if a receipt is $115 including a 15% sales tax, the pre-tax price is $115 ÷ 1.15 = $100.