Euler's Method Calculator
Step a differential equation forward one interval at a time.
Enter your values
ⓘ Live results
Results
- Next y (Euler)
- 1.1
- Next x
- 0.1
- Change in y
- 0.1
- Improved Euler (Heun)
- 1.105
- Euler vs Heun gap
- 0.005
Quick answer
Euler's method steps a differential equation forward using the slope at the current point: y next = y + h × f(x, y).
yₙ₊₁ = yₙ + h·f(xₙ, yₙ)
How to use the Euler's Method Calculator
- 1Enter the current x and y of your solution.
- 2Enter the slope f(x, y) from your differential equation.
- 3Choose a step size, then feed the new point back in for the next step.
Worked example
Using the values the calculator loads with:
Inputs
- Current x0
- Current y1
- f(x, y) — the slope here1
- Step size h0.1
- Slope at the predicted point (optional, for Heun)1.1
Results
- Next y (Euler)1.1
- Next x0.1
- Change in y0.1
- Improved Euler (Heun)1.105
- Euler vs Heun gap0.005
Frequently asked questions
How small should h be?
Small enough that halving it barely changes the answer. Euler's error is proportional to h, so it needs smaller steps than higher-order methods.
What is Heun's method?
A predictor-corrector: average the slope at the start with the slope at the Euler-predicted point for far better accuracy.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.