What is a percentage?

A percentage is a number or ratio expressed as a fraction of 100. The word percent comes from the Latin ‘per centum’ meaning ‘by the hundred’. So 25% means 25 out of every 100, or the fraction 25/100, or the decimal 0.25. Percentages are used everywhere: discount sales (20% off), interest rates (8% per year), exam scores (85%), statistical reports, tax rates, growth metrics, recipe scaling, and more. This calculator handles the three most common percentage calculations: finding X% of a number, expressing one number as a percentage of another, and calculating the percentage change between two values – all instantly with worked formulas shown.

How to use this tool

1. Choose calculation mode — Three modes available: ‘X% of Y’ (find a percentage of a number), ‘X is what % of Y’ (express one as percentage of another), ‘% Change’ (find percentage increase or decrease).
2. Enter values — Based on mode, enter 1-2 numbers. The calculation happens instantly.
3. Read result — Big number shows the answer. Subtitle shows the math formula used.
4. Switch modes if needed — Different real-world questions need different modes. Read the labels carefully to pick the right one.

Three percentage calculations explained

1. X% of Y (most common):

X% of Y = (X / 100) × Y

Example: 20% of 500 = (20/100) × 500 = 100

2. X is what % of Y (reverse):

X is (X / Y) × 100 percent of Y

Example: 100 is what % of 500? = (100/500) × 100 = 20%

3. Percentage Change (increase or decrease):

% Change = (New – Old) / |Old| × 100

Example: From 50 to 75 is (75-50)/50 × 100 = 50% increase

Examples

X% of Y mode:

• 30% of 250 = 75 (e.g. discount of 30% on a ₹250 item saves ₹75)
• 15% of 80 = 12 (tip amount on $80 bill = $12)
• 5% of 1,200 = 60 (GST of 5% on ₹1,200 = ₹60)
• 72% of 500 = 360 (a student scoring 72% out of 500 marks = 360 marks)

X is what % of Y:

• 425 is what % of 600? = 70.83% (exam result 425/600)
• 15 is what % of 200? = 7.5% (15 free hours out of 200 = 7.5% time saved)
• 200 is what % of 5,000? = 4% (rebate of ₹200 on a ₹5,000 purchase = 4% off)

% Change:

• From 50 to 65 = 30% increase
• From 100 to 80 = 20% decrease
• Stock went from ₹1,200 to ₹1,500 = 25% gain
• Salary from ₹50K to ₹65K = 30% hike

Tips & best practices

• 10% of any number is just moving the decimal one place left: 10% of 850 = 85.0
• 20% = 10% × 2; 5% = 10% / 2 – useful mental math shortcuts
• Percentage of percentage isn’t additive: 50% off then 20% off = total 60% off (not 70%) – you’re computing 80% of 50% = 40% of original
• For percentage change above 100% (e.g. tripled = 200% increase), the formula still applies
• When percentage change is negative (loss), use absolute value for direction interpretation
• Compound percentage problems need step-by-step calculation – don’t try to do everything in one formula
• Always note WHICH value is the ‘original’ or ‘old’ – it affects which formula applies

Limitations & notes

Percentage math is straightforward but interpretation can be tricky. Common confusion: percentage points vs percentages. If a tax rate goes from 18% to 22%, that’s a 4 percentage point increase OR a 22% relative increase (4/18). News articles often blur this. For statistical reporting, always specify whether you mean absolute change (percentage points) or relative change (percent).

Frequently Asked Questions

What is the formula for percentage?

Percentage = (Part / Whole) x 100. For example, if you scored 85 out of 100 in a test, your percentage is (85/100) x 100 = 85%. To find X% of a number, multiply the number by X/100.

How do I calculate a discount?

Sale price = Original price – (Original price x Discount % / 100). Example: 25% off ₹1,200 = 1,200 – (1,200 x 0.25) = ₹900. You save ₹300.

How do I calculate percentage increase?

% Increase = (New – Old) / Old x 100. Example: salary went from ₹50,000 to ₹60,000 = (60000-50000)/50000 x 100 = 20% increase.

How do I find the original price after discount?

Original = Sale Price / (1 – Discount%/100). Example: if a 20% discount makes the price ₹800, original = 800/(1-0.20) = 800/0.80 = ₹1,000.

What does 100% mean?

100% means the entire thing – the whole. 100% of 50 is 50. Going beyond 100% means more than the original – 150% is one and a half times the original.

Can I have a negative percentage?

Yes – negative percentage usually means a decrease or loss. -10% means 10% reduction. In percentage change calculations, a negative result indicates the new value is less than the old.

What’s the difference between percent and percentage points?

Percent is a relative measure (X% of Y). Percentage points are absolute differences between percentages. If a rate goes from 5% to 7%, that’s 2 percentage points up OR 40% increase (2/5). Most confusion in news headlines comes from mixing these.

Related tools

Percentage Change · GST Calculator · Discount Calculator