Secant Method Calculator
Find a root of f(x)=0 using the secant method — no derivative needed.
About Secant Method Calculator
The secant method approximates Newton's method by replacing the derivative with a finite difference: f'(xₙ) ≈ [f(xₙ) − f(xₙ₋₁)]/(xₙ − xₙ₋₁). It requires two initial guesses rather than one, and converges at rate φ ≈ 1.618 (superlinear) — faster than bisection but slightly slower than Newton's quadratic rate. No derivative computation is needed.
Formula
Secant iteration
x(n+1) = x(n) - f(x(n)) · (x(n) - x(n-1)) / (f(x(n)) - f(x(n-1)))
- x(n)
- Current approximation
- x(n-1)
- Previous approximation
Worked example
With the default values below, Secant Method Calculator returns Root of 2.094551481542. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- x^3 - 2*x - 5
- x₀ (first guess)
- 2
- x₁ (second guess)
- 3
- Tolerance
- 0
- Max iterationsaccepts 1–500
- 100
Results
- Root
- 2.094551481542
- Iterations
- 7
- |f(root)|
- 3.5527 × 10⁻¹⁵
- Status
- Converged
Step by step
- 1Values used
- 2Secant iteration
- 3Root= 2.094551481542
- 4Iterations= 7
- 5|f(root)|= 0.0000
- 6Status= Converged
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 12 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
When should I use secant vs Newton?
Use secant when the derivative is expensive or unavailable. It needs one extra initial point but avoids derivative computation entirely.
Can the secant method fail?
Yes, if the two function values are nearly equal (horizontal secant line) or if the guesses are too far from the root. Bisection is safer as a fallback.