Learning hub

Percentage calculation guides

These guides are organised by calculation type. Each one explains the concept, gives the formula, works through an example, and links to the interactive calculator so you can apply what you have learned immediately.

Useful starting points

Choose the resource or calculator that best matches what you need to find.

Core percentage calculators

Start here if you are new to percentage calculations or want a single tool that handles the most common questions. The main percentage calculator at the homepage handles three scenarios: finding a percentage of a number, converting a part-and-whole pair into a percentage, and measuring change between two values.

What is X% of Y? Calculator

Enter any percentage and any number to find the corresponding amount. The formula is (percentage / 100) × value. This covers tips, commissions, discounts, and any situation where you apply a rate to a total.

Open the X% of Y calculator

Core Percentage Calculator

Handles all three general percentage questions in one place. Use it when you are not sure which specific calculator to reach for.

Open the core calculator

Percentage change guides

Percentage change questions always involve a before value and an after value. The key rule is that the 'before' value — the original — is always the denominator. Getting this wrong is the most common source of errors.

Percentage increase guide

When a value grows, the increase as a percentage is ((new − original) / original) × 100. Example: a rise from £200 to £230 is a 15% increase.

Open the percentage increase calculator

Percentage decrease guide

When a value falls, the decrease as a percentage is ((original − new) / original) × 100. Example: a fall from £200 to £160 is a 20% decrease.

Open the percentage decrease calculator

Percentage difference guide

When comparing two peer values, the difference is |value1 − value2| / ((value1 + value2) / 2) × 100. The symmetric formula avoids choosing one value as the baseline.

Open the percentage difference calculator

Reverse percentage guide

To find an original value, divide the final value by the multiplier: original = final / (1 ± rate / 100). For a 10% increase, the multiplier is 1.10. For a 10% decrease, it is 0.90.

Open the reverse percentage calculator

Price and tax calculation guides

Discounts, VAT, and sales tax calculations apply percentage arithmetic to prices. These guides cover the specific direction of each calculation — from net to gross, from gross to net, and from full price to sale price — along with real worked examples.

Discount calculator guide

Calculate the saving and the final sale price from an original price and a percentage-off rate. Use it in shops, when comparing deals, and when pricing promotions.

Open the discount calculator

VAT calculator guide

Add VAT to a net price (multiply by 1 + rate/100) or remove VAT from a gross price (divide by 1 + rate/100). Works with any VAT rate.

Open the VAT calculator

Sales tax calculator guide

Calculate the tax amount and the final price inclusive of sales tax for any pre-tax price and tax rate.

Open the sales tax calculator

Reference and deep learning

Once you are comfortable with the individual calculators, the reference pages below provide a broader understanding of percentage maths — useful for studying, teaching, or applying the concepts in new contexts.

Percentage formulas

All ten formulas in one place, each with a definition, the correct baseline to use, worked example, and a note on when it applies and when it does not.

Read all formulas

Worked examples

Over ten fully worked numerical examples across all the main calculation types, including discount, VAT, reverse percentage, and percentage difference.

Browse worked examples

Frequently asked questions

Plain-language answers to the most common percentage questions, from basic calculations through to edge cases involving zero, negative values, and rounding.

Read the FAQ

Blog

Additional guides and deeper explanations beyond the core calculator pages.

Read the blog

Choose your starting point

Not sure where to begin? The core calculator handles the most common questions, or jump to the formulas page for a complete reference.

Use a focused calculator when your question needs a different baseline or a price-specific formula.