Interactive 2D geometric calculators for circles, rectangles, triangles, trapezoids, parallelograms, ellipses, sectors, and rhombuses with step-by-step working.
Calculate the area of a circle from radius or diameter with formula A = πr². Includes exact π values and step solutions.
Calculate the perimeter around any circle from radius or diameter with step-by-step arithmetic working.
Calculate triangle area from base and height with formula A = 1/2 bh, with full step-by-step working.
Calculate rectangle area, perimeter, and diagonal length from length and width with instant unit conversion.
Calculate square area, perimeter, and diagonal from side length with step-by-step arithmetic working.
Calculate parallelogram area from base length and perpendicular vertical height.
Calculate trapezoid area from parallel bases a and b and perpendicular height with step working.
Calculate rhombus area from diagonals d₁ and d₂ or base and height with step-by-step arithmetic proof.
Calculate pie-slice sector area of a circle from radius and central angle in degrees or radians.
Calculate the curved perimeter arc length of a circle segment from radius and central angle.
Discover why circle area is A = pi r^2. Sector unrolling proof, Archimedes polygon bounds, and worked examples.
Understand the definition of Pi as C / d. Why Pi is irrational and transcendental, history from Babylon to supercomputers, and circle perimeter calculations.
Master all triangle area formulas: A = 1/2 b h, Herons formula from 3 sides, trigonometry SAS formula 1/2 a b sin(C), and coordinate geometry.
Calculate trapezoid area with formula A = 1/2 (a + b) h. Arithmetic steps, median crossbar theorem, and right vs isosceles trapezoids.
Why parallelogram area is base times perpendicular height (A = b h), shear mapping invariance, and comparison to rectangles.
Calculate ellipse area with formula A = pi a b. Understanding semi-major and semi-minor axes, stretch factor from circles, and orbital Kepler mechanics.
Step-by-step circular sector area solver. Formulas A = (theta/360) pi r^2 (degrees) and A = 1/2 r^2 theta (radians), pizza slice geometry, and arc length.
Understand 1D boundary length vs 2D interior coverage. Fencing vs grass lawn analogies, unit conversions, and isoperimetric optimization.
Extend Pythagoras to 3 dimensions. Space diagonal formula d = sqrt(x^2 + y^2 + z^2), 3D Cartesian vectors, and sphere radii proofs.
Calculate straight-line Euclidean distance between two points. Formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2), midpoint formula, and worked examples.
