Free online mathematical tools for students, teachers, and professionals. From basic arithmetic to advanced calculus with step-by-step solutions.
Calculate percentages, percentage increase/decrease, and find what percentage one number is of another.
Calculate NowAdd, subtract, multiply, and divide fractions with step-by-step solutions and simplified results.
Calculate NowAdvanced calculator with trigonometric, logarithmic, and exponential functions for complex calculations.
Calculate NowSolve linear, quadratic, and polynomial equations step by step with detailed working shown.
Calculate NowPerform long division with detailed step-by-step working, showing quotient and remainder.
Calculate NowCalculate probability for single and multiple events, combinations, and permutations.
Calculate NowCalculate volume for spheres, cylinders, cones, cubes, and other 3D geometric shapes.
Calculate NowCalculate mean, variance, standard deviation, and other statistical measures for data sets.
Calculate NowMathematics forms the foundation of countless everyday decisions, from calculating discounts while shopping to understanding mortgage interest rates, measuring for home improvements, and analysing financial investments. Whether you're a GCSE student preparing for exams, an A-Level student tackling advanced topics, or a professional needing quick mathematical solutions, our comprehensive suite of maths calculators provides instant, accurate results with clear step-by-step working.
The UK National Curriculum places strong emphasis on mathematical fluency, reasoning, and problem-solving skills from Key Stage 1 through to A-Level. Our calculators support all three pillars by providing not just answers, but the methods and working behind each calculation, helping students understand the 'why' as well as the 'how'.
Mastering key mathematical formulas is essential for exam success and real-world problem-solving. These formulas appear repeatedly across GCSE and A-Level specifications from all major exam boards including AQA, Edexcel, and OCR.
| Topic | Formula | Example Application |
|---|---|---|
| Percentage of number | (Number x Percentage) / 100 | VAT calculation: 20% of 50 = 10 |
| Percentage change | ((New - Original) / Original) x 100 | Price rise: 80 to 100 = 25% increase |
| Circle area | A = pi x r^2 | Pizza size: r=15cm, A = 706.9 cm^2 |
| Circle circumference | C = 2 x pi x r | Wheel distance: r=30cm, C = 188.5cm |
| Sphere volume | V = (4/3) x pi x r^3 | Ball volume: r=5cm, V = 523.6 cm^3 |
| Cylinder volume | V = pi x r^2 x h | Can capacity: r=4cm, h=12cm, V = 603.2 cm^3 |
| Quadratic formula | x = (-b +/- sqrt(b^2-4ac)) / 2a | Solve ax^2 + bx + c = 0 |
| Pythagorean theorem | a^2 + b^2 = c^2 | Right triangle: 3^2 + 4^2 = 5^2 |
| Compound interest | A = P(1 + r/n)^(nt) | Savings growth over time |
| Standard deviation | sqrt(sum((x - mean)^2) / n) | Data spread analysis |
GCSE Mathematics in England, Wales, and Northern Ireland uses the 9-1 grading scale introduced in 2017, with 9 being the highest grade. Understanding grade boundaries helps students set realistic targets and understand where they stand in their preparation.
Note: Foundation tier caps at grade 5. Students aiming for grades 6-9 must take Higher tier.
Note: Boundaries vary by exam board and year based on difficulty.
A-Level Mathematics builds significantly on GCSE content, introducing new topics and greater depth. The qualification consists of Pure Mathematics (two-thirds of content) plus Applied Mathematics (one-third, typically Mechanics and Statistics).
| Content Area | Key Topics | Weighting |
|---|---|---|
| Pure Mathematics | Algebra, functions, coordinate geometry, sequences/series, trigonometry, exponentials/logarithms, differentiation, integration, vectors | ~67% |
| Statistics | Data presentation, probability, statistical distributions, hypothesis testing | ~15-17% |
| Mechanics | Kinematics, forces, Newton's laws, moments, projectiles | ~15-17% |
Percentages are fundamental to everyday life and appear throughout GCSE and A-Level Mathematics. Understanding different percentage calculations is essential for finance, business, and scientific applications.
Mathematical skills extend far beyond examination halls. Understanding when and how to apply mathematical concepts is crucial for personal finance, professional success, and informed decision-making.
Statistics forms a key part of both GCSE and A-Level Mathematics. Understanding measures of central tendency and spread is essential for data analysis and interpretation.
To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, 25% of 80 = (80 x 25) / 100 = 20. Alternatively, convert the percentage to a decimal (25% = 0.25) and multiply directly: 80 x 0.25 = 20. Our percentage calculator handles all percentage operations automatically with step-by-step working.
To add fractions with different denominators: 1) Find the lowest common denominator (LCD) - the smallest number both denominators divide into evenly. 2) Convert each fraction to an equivalent fraction with the LCD. 3) Add the numerators, keeping the LCD as denominator. 4) Simplify if possible. Example: 1/3 + 1/4: LCD is 12, so 4/12 + 3/12 = 7/12.
The quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a solves any quadratic equation in the form ax^2 + bx + c = 0. Use it when factorisation is difficult or impossible. The discriminant (b^2 - 4ac) tells you about roots: positive = two distinct real roots, zero = one repeated root, negative = no real roots. This is essential for GCSE Higher and A-Level Maths.
GCSE Maths uses grades 1-9 with no fixed percentage pass mark - boundaries vary each year. Grade 4 is a 'standard pass' (roughly equivalent to old C grade), typically requiring 17-25% on Foundation tier or 9-17% on Higher tier. Grade 5 is a 'strong pass' for some purposes. Grade 9 usually requires 75-85% on Higher tier. University requirements typically ask for grade 6 or above.
To convert degrees to radians: multiply by pi/180. To convert radians to degrees: multiply by 180/pi. Key values: 30 degrees = pi/6, 45 degrees = pi/4, 60 degrees = pi/3, 90 degrees = pi/2, 180 degrees = pi, 360 degrees = 2pi. A-Level Maths uses radians extensively for calculus and trigonometry.
Standard deviation measures how spread out data is from the mean. Calculate it by: 1) Find the mean of your data. 2) Subtract the mean from each value and square the result. 3) Find the mean of these squared differences (variance). 4) Take the square root of the variance. Low standard deviation means data clusters near the mean; high means spread out data.
Mean is the arithmetic average: sum all values and divide by count. Median is the middle value when ordered (or average of two middle values). Mode is the most frequent value. Use mean for normally distributed data, median when outliers might skew results (e.g., income data), and mode for categorical data or finding most common values.
GCSE Maths has both calculator and non-calculator papers - typically Paper 1 is non-calculator, Papers 2 and 3 allow calculators. A-Level Maths allows calculators in all papers. You need an approved scientific or graphical calculator - the Casio fx-991EX ClassWiz is popular and allowed by all UK exam boards.