Euler Method Calculator
Solve an ODE numerically using Euler's forward method with step size control.
About Euler Method Calculator
Euler's method is the simplest ODE solver: y_{n+1} = y_n + h·f(x_n, y_n). It advances the solution by one step of size h using the slope at the current point. The method has O(h) global error (first-order), meaning you need many small steps for accuracy. It's excellent for teaching but RK4 is preferred in practice.
Formula
Euler step
y(n+1) = y(n) + h · f(x(n), y(n))
- h
- Step size (xTarget - x0)/steps
- f(x,y)
- Right-hand side of ODE
Worked example
With the default values below, Euler Method Calculator returns y(target x) of 3.40962766. Change any input above and every figure here is recalculated in your browser.
Inputs used
- dy/dx = f(x, y)
- x + y
- Initial x₀
- 0
- Initial y₀
- 1
- Target x
- 1
- Stepsaccepts 1–10,000
- 100
Results
- y(target x)
- 3.40962766
- Step size h
- 0.01000000
- Steps used
- 100
Step by step
- 1Values used
- 2Euler step
- 3y(target x)= 3.40962766
- 4Step size h= 0.01000000
- 5Steps used= 100
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is Euler's method less accurate than RK4?
Euler uses only the slope at the start of each step (first-order). RK4 samples the slope at four points per step, achieving O(h⁴) accuracy vs O(h) for Euler.
When might Euler's method be preferred?
For quick estimates, stiff equation detection, or when implementing in hardware with limited computation. It's also used as a building block in more complex adaptive schemes.