Euler's Method Calculator
Step a differential equation forward one interval at a time.
Enter your values
Enter the current x you are working with.
Enter the current y you are working with.
Enter the f(x, y) — the slope here you are working with.
Enter the step size h you are working with.
Enter the slope at the predicted point (optional, for heun) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Step a differential equation forward one interval at a time. |
|---|---|
| Category | Math |
| Inputs needed | Current x, Current y, f(x, y) — the slope here, Step size h, Slope at the predicted point (optional, for Heun) |
| Main output | Next y (Euler) |
| Formula | yₙ₊₁ = yₙ + h·f(xₙ, yₙ) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Current x
- Enter the current x you are working with.
- Current y
- Enter the current y you are working with.
- f(x, y) — the slope here
- Enter the f(x, y) — the slope here you are working with.
- Step size h
- Enter the step size h you are working with.
- Slope at the predicted point (optional, for Heun)
- Enter the slope at the predicted point (optional, for heun) you are working with.
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.
What do I need to enter into the Euler's Method Calculator?
Just 5 values: current x, current y, f(x, y) — the slope here, step size h, slope at the predicted point (optional, for heun). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Euler's Method Calculator work out the answer?
Euler's method steps a differential equation forward using the slope at the current point: y next = y + h × f(x, y). It applies the formula yₙ₊₁ = yₙ + h·f(xₙ, yₙ) and shows the working so you can check each step by hand.
Is the Euler's Method Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.