The Runge-Kutta 4th Order Method (RK4) is one of the most widely used and highly accurate numerical methods for solving ordinary differential equations (ODEs) of the form $y' = f(x, y)$.

It achieves 4th-order accuracy $\mathcal{O}(h^4)$ matching the Taylor series expansion up to $h^4$ without requiring explicit evaluation of higher-order analytical derivatives.

Interactive Runge-Kutta 4th Order Calculator

Runge-Kutta 4th Order (RK4) Solver

Demo

Slope Function $y' = f(x, y)$:

Initial $x_0$:

Initial $y_0$:

Step Size $h$:

Target $x$:

Calculate RK4 Solution