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.
Percentage Increase
Understand how to measure growth from a starting point. Covers salary increases, price rises, and sales growth with the correct baseline.
Read the increase guidePercentage Decrease
Learn how to calculate a reduction as a percentage of the original value. Useful for sale prices, cost cuts, and efficiency metrics.
Read the decrease guidePercentage Difference
Compare two peer values when neither is the starting point. Uses their average as the reference to make the comparison symmetric.
Read the difference guideReverse Percentage
Work backwards from a final value to find the original before a percentage change was applied. Essential for removing tax or reversing a discount.
Read the reverse guideCore 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 calculatorCore 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 calculatorPercentage 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 calculatorPercentage 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 calculatorPercentage 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 calculatorReverse 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 calculatorPrice 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 calculatorVAT 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 calculatorSales 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 calculatorReference 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 formulasWorked examples
Over ten fully worked numerical examples across all the main calculation types, including discount, VAT, reverse percentage, and percentage difference.
Browse worked examplesFrequently 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 FAQBlog
Additional guides and deeper explanations beyond the core calculator pages.
Read the blogChoose 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.
Related percentage calculators
Use a focused calculator when your question needs a different baseline or a price-specific formula.
Percentage Calculator
Find a percentage, percentage ratio, or percentage change.
Percentage Increase Calculator
Measure how much a value has grown from its starting point.
Percentage Decrease Calculator
Work out the percentage reduction from an original value.
Percentage Difference Calculator
Compare two values when neither one is the original baseline.
Reverse Percentage Calculator
Find an original amount from a final value and percentage.
Discount Calculator
Calculate the amount saved and the final sale price.