Created by The Ivy Web
Maths Vault’s student hub is a free set of GCSE and KS3 calculators and practice tools that show full UK-method working in the browser. No account is required. Methods match AQA, Edexcel and OCR-style classroom practice (for example y = mx + c). The steps are algorithmic, not chatbot answers.
Part of Maths Vault, a UK secondary maths platform. Teachers use a separate signed-in area for worksheet generation and Vault Viewer.
Ruler, protractor, compass and tracing paper. No sign-up.
Try Maths whiteboard →How to Calculate Percentage Increase and Decrease: A Step-by-Step GCSE Maths Guide
Percentage increase and decrease is a core topic in GCSE Maths, appearing on all major exam boards like AQA, Edexcel, and OCR. Whether it's calculating a price rise, a discount in a sale, or a change in population, mastering this skill is essential. This guide breaks it down into simple, manageable steps.
The Core Concept: What is a Percentage Change?
A percentage change tells us how much a quantity has grown or shrunk relative to its original value. It's always expressed as a percentage of the original amount. This is a key idea: the "original" or "old" value is our 100% baseline.
The Essential Formula
For any percentage change problem, you can use this single, powerful formula:
** Percentage Change = \frac{Change}{Original} × 100
Where:
Change = New Value – Original Value (this can be positive for an increase, negative for a decrease).
Original = The starting value (100%).
flowchart TD
A[Start: Identify Original & New Values] --> B{Is New > Original?}
B -- Yes --> C[Change = New - OriginalIt is an INCREASE]
B -- No --> D[Change = Original - NewIt is a DECREASE]
C --> E[Apply Formula:Percentage Change = Change / Original x 100]
D --> E
E --> F[State answer with %and 'increase' or 'decrease']
Step-by-Step Walkthrough
Example 1: Calculating a Percentage Increase
A town's population grew from 12,500 to 13,200. What is the percentage increase?
Identify the Original and New values.
Original (Old) = 12,500
New = 13,200
Calculate the Change.
Change = New – Original = 13,200 – 12,500 = 700
Apply the Formula.
Percentage Change = (Change / Original) × 100
= (700 / 12,500) × 100
Calculate.
700 ÷ 12,500 = 0.056
0.056 × 100 = 5.6
State the final answer clearly.
The population increased by 5.6%.
Example 2: Calculating a Percentage Decrease
In a sale, a coat was reduced from £84 to £63. What is the percentage discount?
Identify the Original and New values.
Original = £84
New = £63
Calculate the Change (the discount amount).
Change = Original – New = 84 – 63 = 21
(We use Original – New here because it's a decrease.)
Apply the Formula.
Percentage Change = (21 / 84) × 100
Calculate.
21 ÷ 84 = 0.25
0.25 × 100 = 25
State the final answer clearly.
The coat has a 25% discount.
The Multiplier Method: A Faster Way
For finding a new value after a change, the multiplier method is incredibly efficient and is heavily favoured in GCSE exams.
For an increase of 15%: You find 115% of the original. The multiplier is 1.15 (because 100% + 15% = 115% = 1.15).
For a decrease of 15%: You find 85% of the original. The multiplier is 0.85 (because 100% – 15% = 85% = 0.85).
Example 3: Using the Multiplier for an Increase
Increase £240 by 17%.
Find the multiplier. 100% + 17% = 117% = 1.17
Multiply. New Value = Original × Multiplier = £240 × 1.17
Calculate. £240 × 1.17 = £280.80
Example 4: Using the Multiplier for a Decrease
Decrease 360kg by 12%.
Find the multiplier. 100% – 12% = 88% = 0.88
Multiply. New Value = 360 × 0.88
Calculate. 360 × 0.88 = 316.8 kg
Reverse Percentages: Working Backwards
This is a common exam challenge: "After a 20% increase, a house is worth £240,000. What was its original price?"
The golden rule: Find the multiplier that was used, then divide by it to go backwards.
Example 5: Reverse Percentage Problem
After a 15% discount, a laptop costs £425. What was its original price?
Analyse the change. A 15% discount means you paid 85% of the original price.
Multiplier = 0.85
Set up the equation.
Original Price × 0.85 = £425
Solve by dividing.
Original Price = £425 ÷ 0.85
Calculate.
£425 ÷ 0.85 = £500
Check: 15% of £500 is £75. £500 – £75 = £425. ✓
Common Pitfalls and How to Avoid Them
Confusing Increase and Decrease Multipliers: Always remember: Increase = >1, Decrease =
Start with today’s featured resource above, have a go at the exam question of the day, then explore the tools below. Practise with real data in free football maths and themed maths quizzes. Everything on this hub is free, works in your browser, and shows full step-by-step working.
Download practice booklets that have been checked and signed off. Includes a preview link and an answers link, plus a download count for each booklet.
Simplify surds like √50 and rationalise denominators — step-by-step GCSE working.
Find missing sides and angles in any triangle — step-by-step Higher GCSE working.
Convert a quadratic to completed-square form and find the turning point with full working.
Solve linear inequalities like 3x + 5 < 14 with step-by-step working.
Add, subtract, scalar multiply column vectors and find magnitude — every step shown.
Apply x_{n+1} = ax + b or fractional iteration formulas from a starting value.
Multi-trial probability trees — coins, dice and bags — with or without replacement, plus experiments and Venn diagrams.
Reflect, translate, rotate and enlarge a shape on a coordinate grid — object and image shown.
Drag a 3D cube like the real puzzle. Only whole-layer turns are allowed, so every position is physically possible.
Interactive diagrams and explanations for key GCSE circle theorems (Higher).
Enter class intervals and frequencies — draw a histogram with frequency density bars.
Build and draw pie charts, complete missing angles or frequencies, interpret charts and compare two groups.
Button sequences for standard form, tables, statistics and trigonometry on GCSE calculators.
Solve ax² + bx + c = 0 by factorising when possible, or the quadratic formula — full step-by-step GCSE working.
Expand single brackets like 3(x + 4) or factorise by taking out a common factor — every step explained.
Cuboids, cylinders, triangular prisms and cones — work out volume or surface area with step-by-step formulas.
Find the hypotenuse or a shorter side using a² + b² = c² — labelled triangle diagram and every step explained.
SOH CAH TOA for right-angled triangles: find a missing side or angle with a labelled diagram and step-by-step working.
Gradient, midpoint and the equation y = mx + c from two points — or plot from m and c, with a graph and full working.
Simplify fractions, add, subtract, multiply and divide, or convert between fractions, decimals and percentages — every step shown.
Circumference, area, and finding the radius from C or A — step-by-step using π.
Speed = distance ÷ time and density = mass ÷ volume. Enter two values to find the third with full working.
Paste a list of numbers to get mean, median, mode and range with step-by-step GCSE working.
Find a percentage of an amount, work out increases and decreases, reverse percentages, and percentage change — every step shown.
Simplify ratios, share a total in a given ratio, and solve missing-share problems with full step-by-step working.
Type in two brackets like (x+6)(x+7) and get a full walkthrough with the FOIL method and grid method. No more guessing—see every step.
Stuck factorising? Enter your quadratic (e.g. x²+13x+42) and we’ll show you step-by-step how to factorise it—or use completing the square if it doesn’t factorise nicely.
Enter a quadratic (e.g. x²−4x+3) and use completing the square to find the turning point, y-intercept and x-intercepts, with a labelled graph.
Got a sequence (or a term-to-term rule)? Paste in your numbers or your nth term and we’ll work out the formula step by step, find the 67th term, and tell you if a number is in the sequence.
Explore any number: place value, prime factors, divisors, sum of digits, Roman numerals, binary and more. Handy for number facts and “number of the day” style practice.
Choose a shape (square, rectangle, triangle, trapezium, circle, L-shape), add dimensions, and get step-by-step area and perimeter—or find a missing side from a given area or perimeter.
Convert to and from standard form, and add, subtract, multiply and divide with step-by-step working. Covers same and different powers of 10.
Solve two linear equations, or a line with a circle (x² + y² = …) or parabola, with exact answers and step-by-step elimination or substitution working.
Live exchange rates (ECB) or enter your own rate. Convert between GBP, USD, EUR and 30+ currencies—useful for real-world maths and problem-solving.
Upload an image or diagram, then place and rotate a virtual mirror to find lines of symmetry. See the reflection in real time—great for symmetry topics.
Ruler, protractor, a compass that works like a real compass, and usable tracing paper. Draw constructions and diagrams—no sign-up.
Five daily GCSE retrieval questions — choose Bedrock, Cornerstone, Lintel or Capstone. One from each strand. Today's set only. Free, no sign-up.
Free flashcard sets by topic for Foundation and Higher: Number, Algebra, Ratio, Geometry, Statistics & probability. Tap to flip—read-only, no sign-up.
View the first 1 to 1,000,000 digits of pi, then search for any number—your birthday, 314 for Pi Day (March 14), or any digit sequence. We highlight matches and show positions. Great for Pi Day activities.
Filter by topic—national, global, politics, environment, sport, local—from many UK RSS sources. Stories are scored for statistics and mathematical hooks. No sign-up.
Your fan hub for FIFA World Cup 2026 — today’s matches, group tables, latest results, headlines and top scorers. There’s also a free maths quiz built on live tournament data. No sign-up.
Free GCSE maths quizzes built around topics pupils care about — GCSE leavers, UK weather, esports, music, Pokémon TCG and more. Data-driven multiple-choice questions; members can download printable worksheets and PDFs.
Free maths quiz and printable worksheet using real Premier League and Championship league table data. Practise points, goal difference, averages and percentages with live standings—do the quiz online or download a PDF worksheet. No sign-up.
Step-by-step walkthroughs of common topics and exam-style questions. Diagrams, worked examples and revision-friendly posts—free to read.
No. The calculators, Keystones, quizzes and blog walkthroughs on this page work in your browser with no account.
UK-method working used on AQA, Edexcel and OCR GCSE Mathematics (for example y = mx + c and SOH CAH TOA). They are not official exam-board papers.
No. These student tools show algorithmic working: programmed steps, not chatbot answers.
Yes for this student hub. Teacher worksheet generators on Maths Vault are a separate signed-in product with a free tier and paid plans.