Bezier Curve Point Calculator

About this calculator

A quadratic Bezier curve is defined by three control points — a start point P0, a control point P1 that pulls the curve toward it without the curve actually touching it, and an end point P2 — and a parameter t that sweeps from 0 to 1 along the curve. The point at any t is found with B(t) = (1−t)² × P0 + 2(1−t)t × P1 + t² × P2, a weighted blend where the weights are the terms of a binomial expansion, which is why the curve always stays within the triangle (convex hull) formed by the three control points.

This exact math underlies vector graphics formats like SVG and PostScript/PDF paths, font outline definitions (TrueType uses quadratic Beziers directly), CAD curve modeling, and animation easing curves, because designers and engineers need a compact way to describe smooth curves with just a few numbers. Enter the three control points and a t value between 0 and 1 to find the corresponding (x, y) point on the curve.