Free Tool

Reverse Percentage Calculator

Find the original number when you know a percentage of it, or the value before a price rise or discount. The formula and each step are shown with the answer.

Free
· No signup
· Step-by-step working
· Runs in your browser

Private by design. Calculations run in your browser; the numbers you enter are not sent to Q3 Labs.

Original value

Enter the known value and the percentage to find the original value.

What is a reverse percentage calculator?

Reverse percentage calculations help you find the original number when you know a percentage of that number. A normal percentage question goes forwards: what is 40% of 200? A reverse percentage question goes backwards: 80 is 40% of what?

You meet this every day: the price before a discount, a salary before a raise, a price before tax, or a full target when you know how much of it you've reached. The calculator answers all of these and shows the working, so you can check it or learn the method.

How to calculate the original value

You know that 60 is 30% of the original amount.

Convert the percentage to a decimal: 30 ÷ 100 = 0.30.
Divide the known value by that decimal: 60 ÷ 0.30 = 200.

So the original value is 200. Check it by going forwards: 30% of 200 is 60.

Reverse percentage formula

Original = Known value ÷ (Percentage ÷ 100)

After a P% increase: Original = Known value ÷ (1 + P ÷ 100)

After a P% decrease: Original = Known value ÷ (1 − P ÷ 100)

All three are the same idea: work out what share of the original the known value is, then divide by that share. After a 20% decrease, what remains is 80% of the original; after a 20% increase, the new value is 120% of the original.

Step-by-step example

If 80 is 40% of a number:

Original = 80 ÷ (40 ÷ 100)

Original = 80 ÷ 0.4

Original = 200

Reverse percentage vs percentage increase

A percentage increase goes forwards: 100 increased by 10% is 110. The reverse question starts from 110 and asks what it was before the 10% increase. Because the new value is 110% of the original, divide by 1.1: 110 ÷ 1.1 = 100.

Taking 10% off 110 gives 99, not 100. That's the most common mistake: the 10% was 10% of the original, not of the new value.

Reverse percentage vs percentage decrease

A price falls 20% from 100 to 80. To recover the original, remember that 80 is what's left: 100% − 20% = 80% of the original. So the original is 80 ÷ 0.80 = 100.

Adding 20% back to 80 gives 96, which is wrong. The 20% was 20% of 100, a bigger number than 80, so you can't undo it by taking 20% of the smaller number.

Finding an original price after a discount

A jacket costs 60 in a 25% off sale. You paid 75% of the original price, so the original was 60 ÷ 0.75 = 80. In the calculator, choose "X is after a P% decrease" and enter 60 and 25, or choose "X is P% of the original" and enter 60 and 75. Both give the same answer.

The same method removes tax from a price that includes it. A price of 119 including 19% VAT is 119% of the price before tax: 119 ÷ 1.19 = 100.

Common reverse percentage examples

Reverse percentage examples with the working and the original value
Situation	Working	Original
A sale price of 60 after 25% off	60 ÷ 0.75	80
A salary of 52,500 after a 5% raise	52,500 ÷ 1.05	50,000
A price of 119 including 19% VAT	119 ÷ 1.19	100
340 units sold is 85% of the target	340 ÷ 0.85	400
36 students is 12% of the school	36 ÷ 0.12	300
This year's 150 sales are 250% of last year's	150 ÷ 2.5	60

The last example is above 100%: when the known value is bigger than the original, the percentage is over 100.

Frequently Asked Questions

What is a reverse percentage?

A reverse percentage works backwards from a percentage to the original amount. Instead of asking "what is 40% of 200?" (80), you ask "80 is 40% of what?" (200).

How do I find the original number from a percentage?

Divide the known value by the percentage written as a decimal. If 80 is 40% of a number: 40 ÷ 100 = 0.4, then 80 ÷ 0.4 = 200.

What is the reverse percentage formula?

Original = Known value ÷ (Percentage ÷ 100). After an increase of P%, divide by (1 + P ÷ 100); after a decrease of P%, divide by (1 − P ÷ 100).

How do I find the original price after a discount?

Work out what percentage you paid, then divide by it. After 25% off you paid 75% of the original, so a sale price of 60 was 60 ÷ 0.75 = 80. Choose "X is after a P% decrease" and enter 60 and 25.

Why can't I just add the percentage back?

Because the percentage was taken from the original, not from the reduced value. 100 minus 20% is 80, but 80 plus 20% is 96, not 100. The correct way back is 80 ÷ 0.8 = 100.

Can the percentage be more than 100%?

Yes. If 50 is 200% of a number, that number is 50 ÷ 2 = 25. A known value bigger than the original simply means the percentage is over 100.

Why can't the percentage be 0%?

Zero percent of any number is 0, so 0% gives no information about the original; mathematically it would mean dividing by zero. The calculator shows a message instead of a result.

Can I use negative numbers?

The known value can be negative (for example a loss), and the result will be negative too. The percentage must be positive: to work back from a fall in value, choose "X is after a P% decrease" rather than entering a negative percentage.

Can I use decimals?

Yes, in both fields, for example 19.99 and 12.5%. Commas as thousands separators (1,250.50) and a % sign are accepted. 19.99 is 80% of 24.9875.

How accurate is the result?

The calculation uses standard double-precision arithmetic, accurate to about 15 significant digits, and the result is shown rounded to 12 significant digits so floating-point noise never appears. Copy Result copies that rounded value without thousands separators.

How do I check the answer?

Multiply the original by the percentage. The calculator shows this check under every result, for example "Check: 40% of 200 = 80".

Are my numbers saved or sent anywhere?

No. The calculation runs in your browser; the numbers you enter are not sent to Q3 Labs or stored.

Is this calculator free?

Yes. It is free and needs no account.

Explore more

Going the other way, from an original price to a sale price? Use the Percent Off Calculator, and work out profit, margin and markup with the Profit Margin Calculator. Work out a new salary or a raise percentage with the Salary Increase Calculator. Estimate what search traffic could be worth with the SEO ROI Calculator, or browse all our free tools.

Keep exploring

Related services

eCommerce MarketingGeneric marketing playbooks miss the details that actually move eCommerce revenue: margin, AOV, and repeat pu…
eCommerce Website Development DubaieCommerce website development for Dubai and UAE brands, with AED pricing, regional payment gateways and Arabi…
Custom eCommerce Website DevelopmentCustom eCommerce website development for complex catalogs, B2B pricing and multi-region storefronts, built on…
Shopify DevelopmentShopify is the right call when you want a managed, PCI-compliant checkout and a mature app ecosystem without…
Web DevelopmentSlow, hard-to-maintain websites quietly cap growth by hurting Core Web Vitals, SEO, and conversion rate.

Case studies

Craftly MarketplaceSEO + Paid Social

Tools

QR Code GeneratorCreate and download free QR codes for URLs, text, Wi-Fi, email, contacts and more.