Bisection Method Calculator

This page contains an online interactive calculator to find out the root of a non-linear equation using the bisection method with step-wise calculations and explanations. You can visit the Bisection Method page to get a detailed explanation.

Given,

$y=f(x)=$

Interval: $a =$to$b =$

Error threshold$(e)=$

Solution,

Check whether the interval brackets a solution:

$$f(a)=f(1)=(1)^3-2=-1$$

$$f(b)=f(2)=(2)^3-2=6$$

Since $f(a)\times f(b)=-6\leq 0$, the interval brackets a solution and hence we can proceed further.

$n$	$a$	$b$	$f(a)$	$f(b)$	$x_n=(a+b)/2$	$f(x_n)$	Assign
$1$	$1.000$	$2.000$	$-1.000$	$6.000$	$1.500$	$1.375$	$b=x$
$2$	$1.000$	$1.500$	$-1.000$	$1.375$	$1.250$	$-0.047$	$a=x$
$3$	$1.250$	$1.500$	$-0.047$	$1.375$	$1.375$	$0.600$	$b=x$
$4$	$1.250$	$1.375$	$-0.047$	$0.600$	$1.313$	$0.261$	$b=x$
$5$	$1.250$	$1.313$	$-0.047$	$0.261$	$1.281$	$0.103$	$b=x$
$6$	$1.250$	$1.281$	$-0.047$	$0.103$	$1.266$	$0.027$	$b=x$
$7$	$1.250$	$1.266$	$-0.047$	$0.027$	$1.258$	$-0.010$	$a=x$
$8$	$1.258$	$1.266$	$-0.010$	$0.027$	$1.262$	$0.009$	$b=x$
$9$	$1.258$	$1.262$	$-0.010$	$0.009$	$1.260$	$-0.001$	$a=x$
$10$	$1.260$	$1.262$	$-0.001$	$0.009$	$1.261$	$0.004$	$b=x$

Therefore, the solution is at $x=1.261$