Pick a shape, enter its dimensions, get area / perimeter / volume with the formula used.
How this works: each shape has a fixed area/volume formula. Enter the shape's dimensions above and the calculator substitutes your numbers directly into the formula so you can see each step, and get the final figure.
Square — Area = side² · Perimeter = 4 × side
Rectangle — Area = l × w · Perimeter = 2(l + w)
Triangle — Area = ½ × base × height
Circle — Area = πr² · Circumference = 2πr
Trapezoid — Area = ½ × (a + b) × height
Cube — Volume = side³ · Surface Area = 6 × side²
Cuboid — Volume = l × w × h · Surface Area = 2(lw + wh + hl)
Cone — Volume = (1/3)πr²h · Surface Area = πr(r + l), where l = √(r² + h²)
Example: a cylinder with radius 3 cm and height 7 cm →
Volume = π × 3² × 7 = π × 9 × 7 ≈ 197.92 cm³.
Surface Area = 2π × 3 × (3 + 7) = 2π × 3 × 10 ≈ 188.5 cm².
Roots & Powers
Square root, cube root, nth root, or raise a number to a power.
How this works: a square root of x is the value that, multiplied by itself, equals x. A cube root multiplies itself three times. An nth root generalizes this as x^(1/n), and a power raises x to any exponent n.
Find a percentage of a number, a percentage increase/decrease, or what % one number is of another.
How this works: percentage problems come in three common forms, each with its own formula.
X% of Y = (X / 100) × Y
% change from A to B = ((B − A) / A) × 100
A is what % of B = (A / B) × 100
Example: 20% of 150 = (20/100) × 150 = 30.
A price rising from 80 to 100: change = ((100−80)/80) × 100 = 25% increase.
45 out of 60 marks: (45/60) × 100 = 75%.
Quadratic Equation Solver
Solves ax² + bx + c = 0 using the quadratic formula, step by step.
How this works: the quadratic formula solves any equation of the form ax² + bx + c = 0. The discriminant (b² − 4ac) determines the root type.
x = (−b ± √(b² − 4ac)) / 2a
D > 0 → two real, distinct roots
D = 0 → one repeated real root
D < 0 → two complex roots
Example: for x² − 3x + 2 = 0 (a=1, b=−3, c=2):
D = (−3)² − 4(1)(2) = 9 − 8 = 1.
x = (3 ± √1) / 2 → x = 2 or x = 1.
LCM & HCF (GCD)
Enter two or more numbers separated by commas.
How this works: HCF (Highest Common Factor, or GCD) is the largest number dividing all given numbers exactly. LCM (Least Common Multiple) is the smallest number all of them divide into exactly. Both are computed here using the Euclidean algorithm.
HCF(a, b): largest number dividing both a and b with no remainder
LCM(a, b) = (a × b) / HCF(a, b)
Example: for 12 and 18 — factors of 12: 1,2,3,4,6,12; factors of 18: 1,2,3,6,9,18.
HCF = 6. LCM = (12 × 18) / 6 = 216 / 6 = 36.
Right-Triangle Solver
Enter any two known values (angle in degrees and/or two sides) to solve the rest.
How this works: in a right triangle, the trig ratios relate an angle to the ratio of two sides, and the Pythagorean theorem relates all three sides.
Why does this show steps instead of just the answer?
A bare number doesn't help you learn or check a homework method : seeing the formula and substitution lets you verify your work and catch where a manual calculation went wrong.
Are these calculators accurate for exams?
The math is standard and exact, but always follow your exam's required rounding rules and show your own working where marks are awarded for the method, not just the final answer.
Can I use these calculators to double-check homework or exam prep?
Yes, because each tool lays out the formula and the substitution line by line, you can match it against your own worked solution and spot exactly where a manual attempt diverges, rather than only comparing final digits.