Reverse Percentage

Written by Aarav Sharma Reviewed by Vikram Sen Last updated: June 1, 2026 Last verified: June 1, 2026 · Methodology · Accuracy policy

The reverse percentage page (reverse percent) uses one primary formula—enter values using the form labels (rate, base, part, or whole) that match your problem statement.

Tip: For reverse percentage (reverse percent), match each input to the problem statement before you calculate.

Cluster: Basic calculators hub · Complete percentage guide

Undo a percent change. You are given a final value that already reflects a percent increase or decrease applied to an unknown original, and you must recover that original. Story cues include “after a 25% discount you paid $60” or “after an 8% fee was added the invoice reads $324.”

This is different from “30 is 20% of what number?” In that textbook line, 30 is literally the result of taking 20% of the unknown . Here, the final value is usually the whole after the change , not merely the slice named by the percent. If your wording matches the slice interpretation, use find number from percentage instead so the formula matches the story.

Plug the post-change amount and the stated percent into the form. For forward growth (start plus uplift in one forward step), use increase by percentage ; for symmetric cuts, use decrease by percentage .

Original Value

Final Value: *

How Reverse Percentage Works

What is "Reverse Percentage"?

This calculation helps you find the original value of a number before a (like a markup or tax) was added. It allows you to "reverse" the calculation when you only know the final amount and the percentage that was added to it.

Formula

Reverse Percentage Formula (After Increase)

Original Value = Final Value / (1 + Increase% / 100)

Final Value = The amount after the increase

Increase% = The percentage that was added

Original Value = The starting number you're looking for

Step-by-Step Example

Problem: A product costs $120 after a 20% markup. What was the original cost?

Given:
Final Value = $120
Markup = 20%

Step 1: Convert increase to a multiplier
1 + (20 / 100) = 1.20

Step 2: Divide the final value by the multiplier
Original = $120 / 1.20 = $100

Answer: The original price was $100.

🎯 Tips & Common Mistakes

Don't just subtract the percentage: If a price increased by 20%, you cannot find the original by subtracting 20% from the final price. This is because 20% of the final price is larger than 20% of the original.
Markup vs. Discount: This formula assumes an increase. If you are calculating for a discount, you would use (1 - Percentage / 100) as your divisor.

Finding the Original

Reverse percentage helps you find the original value before a percentage was applied. It's essential for removing taxes from prices, finding pre-discount amounts, and recovering original costs.

The Reverse Formula

After Increase: Original = Final / (1 + Rate/100)
After Decrease: Original = Final / (1 - Rate/100)
Example: $115 after 15% increase → $115 / 1.15 = $100

Tax-Inclusive Pricing

Many countries display tax-inclusive prices. To find the pre-tax amount: divide by (1 + tax rate). At 8% tax, an $80 total means about a $74.08 base price. This is not the same as subtracting 8% from $80; that would give $73.60, which is incorrect.

❓ Frequently Asked Questions

What is a reverse percentage?

It is finding the original value after a percentage increase or decrease has been applied. You are 'reversing' the change.

How do I calculate the original price after a discount?

Divide the current price by (1 - discount rate as a decimal). If a shirt is after a 20% discount, calculate 20 / 0.8 = .

Why can't I just add the percentage back?

Because the percentage was taken from the *original* higher amount, not the new lower amount. Adding 20% to () won't get you back to .

🔍 Authoritative References

For more information about basic percentage calculations, consult these trusted sources:

National Council of Teachers of Mathematics - Mathematics education standards
Math is Fun - Clear mathematical explanations and examples