Reverse Percentage Calculator

Reverse percentage flips the usual question around. Forward percentage asks "15% of 200 is how much?"; reverse asks "30 is 15% of how much?" You know a part and the percentage it represents — the whole is the unknown. It is the most frequently needed percentage problem that most people never formally learned, and it resurfaces in tax-inclusive pricing, marks, commissions and budgeting.

The formula

Original = known value × 100 ÷ percent

Worked example

30 is 15% of what?

30 × 100 ÷ 15 = 3000 ÷ 15 = 200

So 30 is 15% of 200.

Why it works

"30 is 15% of X" is the statement X × 0.15 = 30. Solve it algebraically:

X = 30 ÷ 0.15 = 200

Multiplying by 100 and dividing by the percent-as-a-whole-number is exactly the same arithmetic in different clothes: 30 × 100 ÷ 15.

Real uses

• Inclusive pricing and tax — a price of ₹11,800 that already contains 18% GST is not "₹11,800 × 0.82". The pre-GST value is 11,800 ÷ 1.18 ≈ ₹10,000, because the tax was added onto the base. Reverse reasoning is the only correct route, and it also shows exactly how much tax you are actually paying.
• Scored work — "34 marks is 85% of the total what's the total?" → 34 × 100 ÷ 85 = 40.
• Commissions — "₹7,500 commission at 5% of sales — what were sales?" → 7,500 × 100 ÷ 5 = ₹1,50,000.
• Budgeting — "rent of ₹12,000 eats 30% of income — what is the income?" → 12,000 × 100 ÷ 30 = ₹40,000.

The family of four

Four tools cover the full percentage triangle, distinguished by which piece is missing:

1. Part known, percent known → whole missing: reverse percentage (this tool).
2. Whole known, percent known → part missing: the percentage calculator.
3. Part and whole known → percent missing: the what percent of tool.
4. Two values known → change or difference: the percentage change and percentage difference calculators.

Reversing after an increase or decrease

The same division habit handles questions where a percent acts on an unknown base: a ₹22,000 salary after a 10% raise was 22,000 ÷ 1.10 = ₹20,000, and a ₹1,500 price after a 25% markdown was 1,500 ÷ 0.75 = ₹2,000. Whenever a known percentage is applied to an unknown starting figure, the base is found by dividing — never by subtracting the percent.

Common mistakes and traps

• Dividing instead of multiplying — 30 ÷ 15 gives the meaningless 2 instead of the 200 whole.
• Dropping the × 100 and treating the division as the whole — the result then describes a share, not the base.
• Reversing an inclusive price with naive percentage work — "including 18% GST" needs ÷ 1.18, not ÷ (100 − 18), because the 18% was added to the base.
• Using "total" loosely when the percentage refers to only part of it — the part and the whole must reference the same quantity.

Practical tips

• Sanity-check the direction: for any percentage under 100, the whole you find must be larger than the part you started with. A smaller result means the operation went backwards.
• For percentages above 100, the whole is smaller than the part — unusual, but the same formula still holds.
• Cross-verify with the forward operation: once you have a "whole", confirm that percent% of it really equals the known part.

If you already have the whole and simply need a portion, the percentage calculator does the job in one step.