How to Calculate Percentage: 3 Proven Formulas With Worked Examples

How to Calculate Percentage: 3 Formulas + Examples

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Almost every “how to calculate percentage” question is secretly one of three different questions — and each has its own formula. Mix them up and you get wrong answers with total confidence. This guide separates the three, works through each with real computed examples, and ends with the distinction that confuses even professionals: percentage points vs. percent.

You will find a Pakistan board-exam worked example (850 out of 1100), discount math, and increase/decrease calculations — every number actually computed, step by step. For instant answers, our free Percentage Calculator handles all three question types.

Table of Contents

The Three Percentage Questions (Know Which One You’re Asking)

Before any formula, identify your question. Each of these looks similar and uses different math:

  1. “What is 20% of 4,500?” — finding a portion of a known whole (discounts, tips, tax).
  2. “What percentage is 850 of 1,100?” — expressing one number as a share of another (exam marks, market share).
  3. “Prices rose from 1,200 to 1,500 — what is the percentage increase?” — measuring change between two values.

The word “of” is your clue: “X% of a number” is question 1, “X as a percentage of Y” is question 2, and anything with “increase,” “decrease,” “change,” or “growth” is question 3. Classify the question first, and you know exactly how to calculate percentage for that case — the rest is arithmetic. A percentage is just a fraction scaled so the whole equals 100 — “per cent” literally means “per hundred.”

Question 1: What Is X% of a Number?

Formula: (X ÷ 100) × number. Or equivalently: 0.X × number.

Example — shop discount. A jacket costs PKR 4,500 with a 20% discount. How much do you save?

  • 20 ÷ 100 = 0.20
  • 0.20 × 4,500 = 900

You save PKR 900; the jacket costs 4,500 − 900 = PKR 3,600.

Example — exam-style. What is 35% of 1,100 marks? 0.35 × 1,100 = 385. (Useful as a sanity check: 35% is a bit more than a third, and a third of 1,100 is about 367 — 385 passes the smell test.)

The 10% mental-math trick. To find any percentage mentally, start with 10%: move the decimal one place left. 10% of 4,500 = 450. Then 20% is double that (900), 5% is half (225), and 15% is 450 + 225 = 675. Most everyday percentages decompose into 10s and 5s, which makes this the single most useful arithmetic trick in this guide.

Question 2: What Percentage Is X of Y?

Formula: (X ÷ Y) × 100.

Example — Pakistan board exam. A student scores 850 out of 1,100 in the board exams. What is the percentage?

  • 850 ÷ 1,100 = 0.772727…
  • 0.772727… × 100 = 77.27% (rounded to two decimals)

Sanity check: 770 out of 1,100 would be exactly 70%, so 850 landing at 77.27% is in the right neighborhood. (For the full board-exam treatment — subject-wise percentages, grade boundaries, and the marks-to-GPA question — see our marks percentage Pakistan guide and the Marks Percentage Calculator.)

Example — market share. Your shop sold 340 of the 2,000 phones sold in the market this month: 340 ÷ 2,000 × 100 = 17% market share.

The #1 error in this question: dividing in the wrong order. (Y ÷ X) × 100 with the exam numbers gives 1,100 ÷ 850 × 100 = 129.41% — obviously impossible for marks, but in business contexts a wrong-order division produces a plausible-looking wrong number. Always ask: which number is the whole? The whole goes on the bottom.

Question 3: Percentage Increase and Decrease

Formula: ((new − old) ÷ old) × 100. The change goes on top; the original value goes on the bottom — always.

Example — price increase. Cooking oil rises from PKR 1,200 to PKR 1,500 per 5 litres. Percentage increase?

  • Change: 1,500 − 1,200 = 300
  • 300 ÷ 1,200 = 0.25
  • 0.25 × 100 = 25% increase

Example — marks decrease. A student’s percentage drops from 90% to 72%. Percentage decrease?

  • Change: 90 − 72 = 18
  • 18 ÷ 90 = 0.20
  • 0.20 × 100 = 20% decrease

Note what just happened: an 18-point drop from a 90 base is a 20% fall. This is the seed of the percentage-points confusion below — the drop is 18 percentage points but 20 percent.

The asymmetry trap. A 50% increase followed by a 50% decrease does not return you to the start. PKR 1,000 + 50% = 1,500; 1,500 − 50% = 750. You are down 25% overall, because the second 50% is taken from a bigger base. To undo a 25% increase you need a 20% decrease (1.25 × 0.80 = 1.00). Whenever someone quotes symmetric-sounding percentages on a changing base, do the two-step math.

Percentage Points vs. Percent: The Confusion That Matters

This is the distinction that separates people who calculate percentages from people who understand them — and news headlines get it wrong constantly.

Take the exam example from the top: a student’s percentage moves from 77.27% to 82.27%. How much did it rise?

  • In percentage points: 82.27 − 77.27 = 5 percentage points. This is the simple arithmetic difference.
  • In percent: 5 ÷ 77.27 × 100 = 6.47%. This is the change relative to where you started.

Both are correct; they answer different questions. “Percentage points” measures the absolute move on the 0–100 scale. “Percent” measures the move relative to the starting value. A headline saying “pass rates rose 5%” when they went from 77.27% to 82.27% is wrong — they rose 5 percentage points, which is a 6.47% increase. The smaller the starting value, the bigger the gap between the two: a move from 2% to 4% is 2 percentage points but a 100% increase.

Rule of thumb: when the underlying numbers are already percentages, say “percentage points” for the simple difference and reserve “percent” for the relative change. Your readers — and your exam board — will thank you.

How to Calculate Percentage on a Phone Calculator

Most people who search how to calculate percentage just want the phone method. Here it is, for each of the three questions:

  • X% of a number: type the number, tap ×, type the percentage, tap %. On most phones, 4500 × 20 % directly gives 900. (On some calculators you must tap = after %.)
  • X as a percentage of Y: divide first, then × 100. 850 ÷ 1100 = 0.7727, then × 100 = 77.27. Phones have no “percentage of” button for this direction — the division is on you.
  • Percentage change: (new − old) ÷ old × 100. For 1,200 → 1,500: (1500 − 1500... — careful: 1500 − 1200 = 300, ÷ 1200 = 0.25, × 100 = 25.

The % button’s dirty secret: on many calculators it just divides by 100, so 20 % becomes 0.20 and 4500 × 20 % = 900 works — but 4500 − 20 % gives 4499.8 on some phones (subtracting 0.20!) and 3600 on others (subtracting 20% properly). When you learn how to calculate percentage on a phone, test your calculator’s % behavior once with a known answer before trusting it on real money.

How to Calculate Percentage Backwards: Finding the Original Price

The reverse question trips everyone: “the price after a 20% discount is PKR 3,600 — what was the original?” You cannot just add 20% (3,600 × 1.20 = 4,320 — wrong). Here is how to calculate percentage backwards correctly:

Formula: original = sale price ÷ (1 − discount rate). With numbers: 3,600 ÷ (1 − 0.20) = 3,600 ÷ 0.80 = PKR 4,500. Check: 4,500 × 0.80 = 3,600 ✓.

Why adding back fails: the 20% was taken off the original (4,500 × 0.20 = 900), but adding 20% to the sale price computes 3,600 × 0.20 = 720 — a smaller base, a smaller chunk. Percentages are base-sensitive; reversing them means dividing by the complement, not adding the rate. The same logic reverses a percentage increase: “after a 25% rise the price is 1,500” → original = 1,500 ÷ 1.25 = 1,200 ✓.

Once you can go both directions — forward and reverse — you truly know how to calculate percentage, not just one formula. Sale archaeology (“what did this cost before the discount?”), undoing tax, and back-solving exam totals all use the reverse form.

Try It: Calculate Any Percentage

All three question types, one tool: the free Percentage Calculator computes X% of a number, X as a percentage of Y, and percentage increase/decrease — showing the steps, not just the answer. And for board-exam math specifically, the Marks Percentage Calculator (Pakistan) is pre-set for the 850/1100-style totals.

Frequently Asked Questions

How do I calculate 20% of a number?

Multiply the number by 0.20 (which is 20 ÷ 100). For example, 20% of 4,500 = 0.20 × 4,500 = 900. The quick mental version: find 10% (move the decimal one place left) and double it.

What is the percentage formula?

It depends on the question: “X% of a number” = (X ÷ 100) × number; “X as a percentage of Y” = (X ÷ Y) × 100; “percentage change” = ((new − old) ÷ old) × 100. There is no single percentage formula — identify the question first.

How do I calculate percentage increase?

Subtract the old value from the new value, divide by the old (original) value, and multiply by 100. Example: 1,200 → 1,500 is (300 ÷ 1,200) × 100 = 25% increase. The original value always goes on the bottom.

What is the difference between percent and percentage points?

Percentage points measure the simple arithmetic difference between two percentages (77.27% → 82.27% is 5 percentage points). Percent measures the change relative to the starting value (the same move is a 6.47% increase). Use “percentage points” when describing moves on the percentage scale.

What is the easiest way to remember how to calculate percentage?

Memorize the three questions, not one formula: “X% of N” → (X÷100)×N; “X as % of Y” → (X÷Y)×100; “change from old to new” → ((new−old)÷old)×100. If you can sort any percentage problem into one of those three buckets, you know how to calculate percentage for it.