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Percentage Calculator

Four common percentage questions in one tool. Every answer shows the formula and the substitution so you learn as you calculate.

Percentage calculator

What is a percentage and why does it matter?

A percentage is a way of expressing a ratio or fraction as a number out of one hundred. The symbol "%" comes from the Italian per cento ("by the hundred"), which itself comes from Latin. Because percentages normalise all proportions to the same base of 100, they make comparisons effortless: a 15% discount means the same thing on a 50 shirt and a 5,000 mattress, even though the absolute amounts differ enormously. That universality is why percentages appear everywhere — shop discounts, interest rates, statistics, election results, recipe adjustments, exam grades, sports statistics, tax calculations, and more.

Despite their simplicity, percentages trip people up all the time. Mixing up a percent change with a percentage point change, forgetting that a 50% loss needs a 100% gain to recover, misreading "25% of" as "25% off", or calculating the wrong base — these are everyday errors. A calculator that shows the formula and the working, not just the final number, helps build the intuition needed to catch those errors.

How this calculator works — four modes

The calculator supports the four canonical percentage questions, each with its own formula:

  1. What is X% of Y? Formula: (X / 100) × Y. Used for discounts, taxes, commission.
  2. X is what % of Y? Formula: (X / Y) × 100. Used for relative sizes, scores, proportions.
  3. % change from X to Y. Formula: ((Y − X) / X) × 100. Used for price changes, growth rates, before/after comparisons.
  4. X is Y% of what? Formula: X / (Y / 100). Used for reverse discount calculations and working back from a sample.

For a formal reference, see the Wikipedia article on percentages or any middle-school arithmetic textbook. The math is elementary, but the calculator's value is in making sure you pick the right formula for the question you are actually asking.

Worked example

A shop offers 30% off a 120 jacket. What is the sale price?

  • Mode 1: What is 30% of 120? → (30 / 100) × 120 = 36 (the discount).
  • Sale price = 120 − 36 = 84.
  • Check with mode 4: 84 is 70% of what? → 84 / (70 / 100) = 120. Correct.
  • Mode 3 sanity check: % change from 120 to 84 → ((84 − 120) / 120) × 100 = −30%. Consistent.

Seeing the same problem from multiple angles is one of the best ways to build real fluency with percentages.

How to interpret the result

Always double-check that the answer is the right kind of quantity. Mode 1 returns an absolute amount (e.g., 36, not 36%). Modes 2 and 3 return a percentage. Mode 4 returns an absolute amount again. Getting the units right is half the battle. If an answer looks suspicious, try rearranging the question into a different mode to verify — the four modes are algebraically equivalent, just expressed differently.

Pay attention to the direction of percent change. Going from 100 to 150 is a 50% increase; going back from 150 to 100 is a 33.33% decrease. They are not symmetric, because they use different bases. This asymmetry is the source of many popular misconceptions (e.g., "a stock falls 50% then rises 50%" → it is still down 25%).

Common applications

  • Shopping discounts. Mode 1 for the discount amount; mode 4 to check the "original price" on sales items.
  • Grades and test scores. Mode 2 for "I got 47 out of 60, what's my percentage?".
  • Growth rates. Mode 3 for "my revenue went from 80k to 95k, what was the growth?".
  • Survey statistics. Mode 2 again for "324 out of 1,200 respondents said yes".
  • Commission and tips. Mode 1 for "what's 7% of 45,000 in commission?".
  • Tax calculations. Mode 1 for "what's 8% sales tax on 120?" and mode 4 for "this total includes 20% VAT, what was the pre-tax price?".

Common mistakes

  • Confusing percentage points with percent change. An interest rate moving from 2% to 3% is +1 percentage point and +50% relative.
  • Assuming percent changes are symmetric. They are not — a 20% loss requires a 25% gain to recover.
  • Applying a percentage to the wrong base. "30% off then 10% off" is a 37% discount (0.7 × 0.9 = 0.63), not a 40% discount.
  • Using mode 1 when mode 4 is needed. "The discounted price is 84 and the discount was 30%, what was the original?" is a mode 4 question: 84 = 70% of what.
  • Misreading "more than 100%". A 150% increase triples the original; 150% of the original is only 1.5× it.

Using the calculator as a learning tool

Because every answer shows the formula and the numeric substitution, this calculator is a genuine teaching tool for students learning percentages — or adults brushing up on them. Try working a problem by hand first, then using the calculator to check both the answer and the formula you applied. Over time the four modes become second nature, and you will start to spot which one applies to any percentage question that comes up in everyday life.

Frequently Asked Questions

What is a percentage?
A percentage is a way of expressing a number as a fraction of 100. The word literally comes from the Latin per centum, meaning "by the hundred". So 25% means 25 out of every 100, or 0.25, or the fraction 1/4. Percentages are convenient because they let us compare proportions directly without worrying about the size of the underlying whole.
How do I calculate X% of Y?
Multiply X by Y and divide by 100, or equivalently multiply Y by X/100. For example, 15% of 80 is (15/100) × 80 = 0.15 × 80 = 12. The calculator's first mode does exactly this, and shows the substituted formula underneath so you can see the working.
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100: ((new − old) / old) × 100. A positive result is an increase, a negative result is a decrease. For example, going from 80 to 100 is (100 − 80) / 80 × 100 = 25% increase. Going from 100 to 80 is (80 − 100) / 100 × 100 = −20%.
Why is a 50% increase followed by a 50% decrease not the same as the original?
Because each percentage is applied to a different base. Start with 100. A 50% increase gives 150. Now apply a 50% decrease — but to 150, not to the original 100 — and you get 75. This is one of the most common misunderstandings with percentages and shows up everywhere from stock markets to weight loss claims.
What does "X is Y% of what?" mean?
It asks for the missing whole when you know a part and the percentage that part represents. For example, "15 is 25% of what?" means: if 25% equals 15, what is 100%? The answer is 15 / (25/100) = 15 / 0.25 = 60. This mode is useful when working backwards from a discount, a sample, or a proportion.
Can percentages be greater than 100?
Yes. 100% means "the whole thing", so 200% means "twice the original" and 150% means "one and a half times". A 200% increase means the new value is three times the old (100% of the original plus a 200% addition). Be careful to distinguish "200% of" (= 2×) from "a 200% increase" (= 3×) — the wording matters.
What is a percentage point?
A percentage point is the arithmetic difference between two percentages. If an interest rate moves from 5% to 6%, that is a 1 percentage point increase but a 20% relative increase (because 1 is 20% of 5). News reports often confuse the two, and the difference can be huge when rates are small.
Is this calculator suitable for students?
Yes — showing the formula and substitution for every answer makes it genuinely educational rather than just a black box. Students can see not only the answer but which formula applies to each kind of question, which helps build intuition about when to use each form. It does not, however, replace understanding: practise doing a few by hand before leaning on it.