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Percentage Calculator

Percentages show up everywhere — in discounts, interest rates, tax bills, test scores, and investment returns. The problem is that even people who are confident with numbers often pause to double-check their percentage math. This free percentage calculator eliminates that pause. It handles the five most common percentage problems in seconds: finding X% of a number, expressing one number as a…

What this calculator does

The calculator covers all five core percentage modes in one tool. Select your mode, enter the values, and the result appears immediately — along with the full calculation so you can verify the logic. This is especially useful for quick decisions: checking whether a 'sale' price is actually a good deal, verifying the VAT amount on an invoice, confirming a grade percentage before a test result is official, or spotting whether a quoted interest rate is monthly or annual.

How it works

Percentage arithmetic has three basic forms. Finding a part of a whole (e.g. 15% of $240 = $36) uses multiplication. Expressing a part as a percentage of a whole (e.g. 36 is what % of 240 = 15%) uses division. Calculating change between two values (percentage increase or decrease) compares the difference to the original. All three are handled here — just pick the mode that matches your question.

A common mistake is confusing 'percentage points' with 'percent change'. If an interest rate rises from 4% to 5%, that is a 1 percentage-point increase, but it is a 25% increase in the rate itself. The percentage change mode in this tool calculates the relative change, which is what matters most for financial comparisons.

When to use this calculator

Reach for this calculator whenever the mental arithmetic isn't reliable enough to act on — when verifying a quoted discount before purchase, calculating a tip accurately at a restaurant, working out whether a salary increase keeps pace with inflation, or checking whether a tax rate has been applied correctly to an invoice. It is equally useful for students checking exam-percentage calculations, teachers converting raw marks, and anyone building a spreadsheet who wants to verify a cell formula before relying on it.

Common mistakes

The single most common error is confusing percentage points with percent change. A rate rising from 4% to 5% is a 1 percentage-point increase, but a 25% relative increase — and these two numbers are not interchangeable. A second frequent mistake is applying a percentage reduction twice: 'get 20% off, then another 10% off' is not a 30% reduction; the second 10% applies to the already-reduced price, producing an 28% combined discount. Use this calculator to verify the actual result before assuming.

Real-world scenarios

A retailer marks a £85 jacket down by 35% for a sale — the actual saving is £29.75, giving a sale price of £55.25. A student scores 68 out of 85 on a test — that's 80%, not the 68 the raw mark suggests. A business owner sees revenue grow from £120,000 to £153,600 — a 28% increase, not the £33,600 absolute figure. In each case, the percentage gives the comparable, scalable figure that the raw number does not.

Formula

Three core percentage formulas cover every common use case

Part = Whole × (P ÷ 100) | P = (Part ÷ Whole) × 100 | Change% = ((New − Old) ÷ Old) × 100

Formula 1 finds a value (e.g. 15% of $200 = $30). Formula 2 expresses a part as a percentage (e.g. $30 is 15% of $200). Formula 3 measures relative change between two values (e.g. price from $200 to $230 = +15%).

Worked example

A software subscription is

20/year. Your company gets an 18% corporate discount. What is the final price and how much do you save?

  1. Calculate the discount amount: 18% of
    20 =
    20 × (18 ÷ 100) = $21.60
  2. Subtract from the original price:
    20 − $21.60 = $98.40
  3. Verify: $98.40 ÷
    20 × 100 = 82% — confirming you pay 82% of the full price

Result: Final price: $98.40 — you save $21.60 (18% discount verified)

Frequently asked questions

How do I calculate 20% of 350?

Select 'X% of Y', enter X = 20 and Y = 350. The calculator returns 70. The formula is: 350 × (20 ÷ 100) = 70. Alternatively, divide 350 by 5, since 20% = 1/5.

How do I calculate a percentage increase?

Select 'Percentage change', enter the original value first, then the new value. The formula is: ((New − Old) ÷ Old) × 100. For example, a salary going from $50,000 to $55,000 is a 10% increase.

What is the difference between percentage change and percentage points?

Percentage change is the relative difference between two values. Percentage points measure the arithmetic difference between two percentages. If a tax rate rises from 20% to 25%, that is 5 percentage points — but a 25% relative increase in the rate.

How do I reverse a percentage — find the original before a discount?

Use 'X is what % of Y' in reverse. If a discounted price is $60 and the discount was 25%, the original was $60 ÷ (1 − 0.25) = $80. Our reverse percentage calculator handles this directly.

How are percentages used in everyday finance?

Interest rates on loans and savings accounts, VAT and sales tax, investment returns, salary increases, and price discounts are all expressed as percentages. Understanding how to move between a percentage and an actual monetary amount is one of the most useful everyday maths skills.

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