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All 5 Percentage Formulas

Type 1 — % of a number
Result = (P ÷ 100) × N
e.g., 20% of 500 = 100
Type 2 — What % is X of Y
P = (X ÷ Y) × 100
e.g., 45 is what % of 180? = 25%
Type 3 — Reverse percentage
N = X ÷ (P ÷ 100)
e.g., 60 is 30% of what? = 200
Type 4 — % increase
% Change = [(New−Old) ÷ Old] × 100
e.g., 500 → 600 = +20%
Type 5 — % decrease
% Change = [(Old−New) ÷ Old] × 100
e.g., 800 → 600 = 25% decrease

Real-World Uses of Percentages

Salary hike calculation

If your salary goes from ₹50,000 to ₹58,000 — what's the percentage increase? Using Type 4: [(58000−50000) ÷ 50000] × 100 = 16% hike.

Exam score percentage

Got 432 marks out of 600? Using Type 2: (432 ÷ 600) × 100 = 72%.

GST calculation

18% GST on ₹10,000? Using Type 1: (18 ÷ 100) × 10000 = ₹1,800 GST. Total = ₹11,800. Or use ToolNinja's GST Calculator directly.

Discount savings

30% off ₹4,500? Using Type 1: (30 ÷ 100) × 4500 = ₹1,350 saving. You pay ₹3,150. Or use ToolNinja's Discount Calculator.

Percentage Increase vs Decrease

Both use the same formula but the interpretation differs:

  • Positive result = percentage increase (e.g., price went up by 15%)
  • Negative result = percentage decrease (e.g., traffic dropped by 8%)
⚠️ Watch out: A 50% increase followed by a 50% decrease does NOT return to the original value. Example: 100 → +50% = 150 → −50% = 75. You're down 25%.

Common Percentage Mistakes

Mistake 1: Adding percentages directly

"My investment grew 20% in Year 1 and 10% in Year 2, so total growth is 30%." Wrong. Actual total = (1.20 × 1.10 − 1) × 100 = 32% cumulative growth.

Mistake 2: Percentage points vs percentages

If interest rates go from 4% to 6%, that's an increase of 2 percentage points — but a 50% increase in the rate itself. These are very different claims.

Mistake 3: Base confusion

Always confirm what the "whole" is. "20% off an additional 10% off" is not the same as 30% off the original price — the second discount applies to the already-reduced price.

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Frequently Asked Questions

Percentage of a number = (Percentage ÷ 100) × Number. For example, 15% of 200 = (15 ÷ 100) × 200 = 30.

Percentage Change = [(New Value − Old Value) ÷ Old Value] × 100. A positive result means an increase, negative means a decrease. For example, ₹500 rising to ₹600: Change = [(600−500) ÷ 500] × 100 = 20% increase.

Percentage = (Part ÷ Whole) × 100. For example, 45 is what percentage of 180? = (45 ÷ 180) × 100 = 25%.

Original Number = Part ÷ (Percentage ÷ 100). For example, 60 is 30% of what number? = 60 ÷ 0.30 = 200.

A percentage is a ratio expressed as a fraction of 100. A percentile is a value below which a given percentage of observations fall — e.g., scoring in the 90th percentile means you scored higher than 90% of test takers. They measure different things.