Enter Inputs
Use explicit multiplication like 2*x, x*(x+1), or 3*sin(x). Trigonometric functions use radians.
Example Data Table
| Equation | x0 | x1 | Tolerance | Max Iterations | Approximate Root |
|---|---|---|---|---|---|
| x^3 - x - 2 | 1.000000 | 2.000000 | 0.000001 | 25 | 1.521380 |
| cos(x) - x | 0.500000 | 1.000000 | 0.000001 | 25 | 0.739085 |
| exp(-x) - x | 0.000000 | 1.000000 | 0.000001 | 30 | 0.567143 |
Formula Used
xn+1 = xn - f(xn) × (xn - xn-1) / (f(xn) - f(xn-1))
The secant method approximates the derivative with a slope built from two recent points. It avoids direct derivative calculation, which makes it useful when derivatives are unavailable or inconvenient.
This page also tracks absolute step error, relative error, function value at the newest estimate, and the number of iterations used before stopping.
How to Use This Calculator
- Enter the equation in terms of x. Use explicit multiplication, such as 2*x or x*(x+1).
- Provide two different starting guesses. Good guesses near the root usually improve stability.
- Set a tolerance for acceptable error and choose a maximum iteration count.
- Choose a stopping rule based on step size, function value, or both.
- Click Solve Equation to display the result above the form and the full iteration history below.
- Use the export buttons to save the iteration table as CSV or generate a PDF report.
FAQs
1. What does the secant method solve?
It finds an approximate root of a nonlinear equation, meaning a value of x where f(x) becomes zero or very close to zero.
2. Why are two starting values required?
The method builds a secant line through two nearby points. That line estimates the slope used to predict the next root estimate.
3. When is it useful compared with Newton style methods?
It is useful when derivatives are difficult, expensive, or unavailable. The secant method often needs fewer inputs, though convergence may be less reliable.
4. What does tolerance control?
Tolerance sets the acceptable error limit. Smaller tolerance can improve accuracy, but it may require more iterations or expose convergence problems.
5. Why can the solver stop with a small denominator warning?
That happens when consecutive function values become nearly equal. The secant slope becomes unstable, so the next estimate may be unreliable.
6. Can this method fail to converge?
Yes. Poor initial guesses, discontinuities, flat regions, or repeated roots can slow convergence or cause divergence.
7. Which equation functions can I use here?
You can use common functions such as sin, cos, tan, exp, log, log10, sqrt, abs, pow, min, max, and pi().
8. What should I do if the result looks wrong?
Check the equation syntax, use explicit multiplication, try better starting guesses, increase maximum iterations, and review the iteration table for instability.