Euler's Method Calculator

About this calculator

Euler's method is the simplest numerical technique for approximating the solution of an ordinary differential equation when no closed-form solution is available or convenient. For a linear ODE y′ = a·x + b·y with a known starting point, it steps forward in small increments of size h using y_{n+1} = y_n + h·(a·x_n + b·y_n) — at each step, it just follows the tangent line given by the current derivative for one step's length, then recalculates the slope at the new point.

This calculator builds the full step-by-step table so you can see how the approximation evolves, alongside the final estimated point. Euler's method has a local truncation error of O(h²) per step and a global error of O(h), meaning halving the step size roughly halves the total error — it's rarely used for high-precision work in practice (more accurate methods like Runge-Kutta 4 are preferred), but it remains the standard first algorithm taught in numerical analysis because it makes the core idea of numerical ODE solving — approximate the curve using its own slope, one small step at a time — completely transparent.