How to Calculate Percentage — The Five Sums People Actually Need
Pick one of the five modes — of, share, change, add-or-subtract or reverse — and the calculator does the rearranging for you, so you type the two numbers you have and read the number you wanted.
| Percent | Value | Remaining |
|---|---|---|
| 1% | 25 | 2,475 |
| 5% | 125 | 2,375 |
| 10% | 250 | 2,250 |
| 15% | 375 | 2,125 |
| 20% | 500 | 2,000 |
| 25% | 625 | 1,875 |
| 30% | 750 | 1,750 |
| 50% | 1,250 | 1,250 |
| 75% | 1,875 | 625 |
| 90% | 2,250 | 250 |
X% of N = (X ÷ 100) × N. A as a share of B = (A ÷ B) × 100. Percentage change = ((new − old) ÷ |old|) × 100, using the absolute value of the old number so a fall below zero still reads correctly. Add or subtract X% = N × (1 ± X ÷ 100), which is the one-step way to apply a discount or a tax. Reverse: if P is Y% of the unknown, the unknown = (P × 100) ÷ Y.
The five formulas, with real numbers
Percentage questions sound different but reduce to a handful of shapes. The table shows the shape, the formula and a worked example for each; the calculator above has all five as separate modes so you can type your own numbers without rearranging the formula yourself.
| You want | Formula | Example | Steps | Answer |
|---|---|---|---|---|
| X% of N | N × X ÷ 100 | 15% of 2,400 | 2,400 × 15 ÷ 100 | 360 |
| A as a share of B | A ÷ B × 100 | 350 out of 500 | 350 ÷ 500 × 100 | 70% |
| Percent change | (new − old) ÷ old × 100 | 18,000 → 21,600 | 3,600 ÷ 18,000 × 100 | +20% |
| Discount / add % | N × (1 ± X/100) | 25% off 8,000 | 8,000 × 0.75 | 6,000 |
| Reverse | paid ÷ (1 + X/100) | 1,150 after 15% GST | 1,150 ÷ 1.15 | 1,000 |
The two mistakes people actually make
Percent change is not percentage points. Interest moving from 8% to 10% is a rise of two percentage points, but a 25% increase relative to where it started (2 ÷ 8 × 100). News headlines mix these freely; exam marks and discount math never do.
You cannot average percentages that have different bases. Scoring 50% on a 100-mark paper and 80% on a 200-mark paper is not a 65% average — the combined mark is (50 + 160) ÷ 300 = 70%. If you need that sum for a marks sheet, the matric aggregate guide works through it with the calculator.
Reverse percentages — the one nobody expects
A shop says “price after 15% discount: 1,360”. The original is not 1,360 + 15% of 1,360 — the discount was taken off the original, so you divide instead: 1,360 ÷ 0.85 = 1,600. The same move applies to bills with GST added, to test marks after negative marking, and to salary figures quoted “including” a deduction. Whenever the percentage was applied to a number you no longer have, divide by (1 ± the rate) instead of adding the percentage back on.
For money sums specific to Pakistan — zakat, gold value and loan instalments — the zakat calculator, gold weight converter and EMI calculator apply these same formulas with the rupee and tola units already built in.
- Choose the mode — “What is X% of N”, “A is what % of B”, “% change”, “add or subtract %”, or “reverse”.
- Type the numbers you have — The labels change with the mode so you never have to rewrite the formula yourself.
- Read the answer and the formula — Every result shows the exact expression it computed, which is how you check a calculator instead of trusting it.
- Use the quick table — A 1–90% reference grid sits under the modes for the percentages you use constantly.
- Five modes instead of one, because “what is 15% of 2400” and “I paid 1380 after GST, what was the base” are different problems.
- Every answer prints the formula it used, which makes the tool teach the maths rather than hide it.
- The quick table of 1–90 percent covers the lookups people do on a phone calculator.
- No account, no upload and no rounding to whole numbers unless you ask for it.
How to Calculate Percentage — questions
How do I calculate a percentage on a normal calculator?
To find X% of N, type N × X ÷ 100. To find what percent A is of B, type A ÷ B × 100. The percent key on many calculators divides by 100 for you, so 2400 × 15% gives the same 360 without the ÷ 100.
How do I work out the percentage increase between two numbers?
Subtract the old number from the new one, divide by the old number and multiply by 100. From 18,000 to 21,600 that is 3,600 ÷ 18,000 × 100 = 20%.
How do I find the original price before a discount?
Divide the price you paid by one minus the discount rate. Paid 6,000 after a 25% discount? 6,000 ÷ 0.75 = 8,000. This is the “reverse” mode in the calculator.
What is the difference between percentage and percentage points?
Percentage points are the simple subtraction of two percentages: 8% to 10% is 2 points. Percent change is relative: 2 ÷ 8 × 100 = a 25% increase. Use points when comparing rates, percent change when something grew or shrank.
Can I average two percentages?
Only if both come from the same total. 50% of 100 marks and 80% of 200 marks average to 70% when combined by marks (210 of 300), not 65% — the 200-mark paper counts double. Combine the raw numbers instead.
How is percentage different from a fraction and a decimal?
They are the same quantity written three ways: 3/4 = 0.75 = 75%. Converting between them is just × or ÷ 100, and the calculator shows the decimal alongside every answer.