Solve f(x) = 0, one geometric step at a time. Watch Newton–Raphson ride the tangent, bisection squeeze a bracket, and the secant method draw chords to the crossing.
Root Finding StudioLive
Newton · bisection · secant
Controls
Function
Method
Solve f(x) = 0. Watch the method step toward the root — Newton rides the tangent, bisection halves the bracket, secant draws chords.
Reading this result: Newton–Raphson converged to x ≈ 2.500000 in 4 iterations (|f(x)| < 1e-6). Near a simple root Newton roughly doubles the number of correct digits each step (quadratic convergence).
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How it works
Root finding locates where a function crosses zero. Newton–Raphson follows the tangent line at the current guess down to the x-axis and converges quadratically near a simple root, but a small derivative or a poor start can send it flying. Bisection needs only a sign change on [a, b] and halves the bracket every step — slow but guaranteed. The secant method replaces Newton's derivative with a finite-difference slope through the last two points, converging superlinearly (order ≈ 1.618) with no calculus required. Pick a preset function, choose a method, and scrub the Step slider to see each iterate.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this Newton bisection root finding tool really free?▾
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How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.