Math, made visual.
Solve, drag, and watch the formulas come to life.

The circumference of a circle is the linear distance around its boundary. Using the radius r, the formula is C = 2 · π · r. With the diameter d = 2r, the equivalent form is C = π · d. Drag the slider below — the SVG circle scales live, and the unroll animation flattens the boundary onto a green ruler ribbon to show what the formula actually measures.

A mixed fraction like 2 1/3 is converted to an improper fraction via (whole × den + num) / den. The solver finds a common denominator, performs the operation, and simplifies using the GCD — every step shown transparently below.

A trapezoid has two parallel bases a (top) and b (bottom) and a perpendicular height h. Its area is the average of the two bases multiplied by the height: A = ((a + b) / 2) · h. The dashed midsegment in the live model marks that average base.

Simple interest is calculated only on the original principal — no compounding. The formula is I = P · r · t where P is the principal, r is the annual rate (decimal), and t is time in years. Watch coins stack as the inputs grow.

Rounding uses the half-up rule: if the digit to the right of your target place is ≥ 5, round up; otherwise round down. Pick a place value, type any decimal, hit Trigger Snapping — gravity pulls the ball down the slope onto the nearest anchor integer.