Math & Geometry

Homework, an engineering estimate or a workshop measurement: basic geometry and algebra formulas are needed constantly but are hard to recall each time. The tools here give the result, show the formula openly and let you follow the steps.

Which tool for which question?

• Area and Perimeter Calculator (Geometric Shapes): Calculate the area and perimeter of a square, rectangle, triangle, circle, trapezoid, parallelogram, rhombus or ellipse, with the area in square metres.
• Factorial, Permutation and Combination Calculator: Calculate n factorial, permutations P(n, r) and combinations C(n, r) exactly (no rounding) for n and r up to 21; a flag shows when r is greater than n.
• Volume and Surface Area Calculator (Cube, Cylinder, Sphere, Cone): Calculate the volume and surface area of a cube, cuboid, cylinder, sphere, cone, square pyramid or frustum, with the volume in m³ and litres.
• Quadratic Equation Solver (ax² + bx + c = 0): Solve ax² + bx + c = 0: discriminant, real or complex roots, the vertex of the parabola and the sum and product of the roots.
• Logarithm Calculator (log, ln, log2 and Antilog): Calculate the logarithm of a number in any base, its natural (ln), common (log10) and binary (log2) logarithm, and the antilogarithm.
• Mean and Standard Deviation Calculator: Calculate the sum, arithmetic mean, population and sample variance, standard deviation, coefficient of variation, minimum, maximum and range of 2 to 10 numbers.
• Pythagorean Theorem Calculator: Find the hypotenuse from the two legs of a right triangle, or the missing leg from one leg and the hypotenuse; also get the area, perimeter and height to the hypotenuse.
• Exponent and Root Calculator (Power, Square Root, Cube Root, n-th Root): Raise a number to any power (including fractional and negative exponents) and take its square root, cube root and n-th root.

How the calculation works

• Area and perimeter depend on the shape; volume and surface area use formulas for solids such as cube, cylinder, sphere and cone. Dimensions must be entered in the same unit.
• Pythagorean theorem: in a right triangle a² + b² = c²; c is the hypotenuse.
• The quadratic equation ax² + bx + c = 0 is solved with the discriminant (b² − 4ac); if it is negative there is no real root.
• Logarithm: bʸ = x ⇔ log_b(x) = y.
• Factorial n! = n × (n−1) × … × 1; permutations count arrangements, combinations count selections without regard to order.
• Mean and standard deviation measure the centre and the spread of data.

Common mistakes

• Entering dimensions in different units (cm and m mix-up).
• Taking a leg for the hypotenuse in Pythagoras.
• Confusing permutation and combination: when order matters, use permutation.