Equation root finder
Equation root finder
Find a numeric root of f(x)=0 on an interval using bisection.
Input
The first endpoint of the search interval. Choose endpoints that bracket the root for the supported interval method.
The stopping tolerance for the numerical root search. A smaller value asks for a tighter approximation within the iteration limit.
Output
Root
1.4142136574
f(root)
2.687177e-7
Iterations
22
#
a
b
mid
f(mid)
3
1
1.5
1.25
-0.4375
4
1.25
1.5
1.375
-0.109375
5
1.375
1.5
1.4375
0.06640625
6
1.375
1.4375
1.40625
-0.02246094
7
1.40625
1.4375
1.421875
0.02172852
8
1.40625
1.421875
1.4140625
-0.00042725
9
1.4140625
1.421875
1.41796875
0.01063538
10
1.4140625
1.41796875
1.41601563
0.00510025
11
1.4140625
1.41601563
1.41503906
0.00233555
12
1.4140625
1.41503906
1.41455078
0.00095391
13
1.4140625
1.41455078
1.41430664
0.00026327
14
1.4140625
1.41430664
1.41418457
-0.000082
15
1.41418457
1.41430664
1.41424561
0.00009063
16
1.41418457
1.41424561
1.41421509
4.314817e-6
17
1.41418457
1.41421509
1.41419983
-0.00003884
18
1.41419983
1.41421509
1.41420746
-0.00001726
19
1.41420746
1.41421509
1.41421127
-6.474773e-6
20
1.41421127
1.41421509
1.41421318
-1.079981e-6
21
1.41421318
1.41421509
1.41421413
1.617417e-6
22
1.41421318
1.41421413
1.41421366
2.687177e-7
Find equation roots online
Use bisection to find a root on an interval where the function changes sign.
The iteration table helps review convergence and detect intervals that need adjustment.
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The tool runs directly in the browser and is ready for quick checks without installing software.
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Input can be cleared and recalculated immediately, which is useful for repeated small tasks.
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Use fullscreen mode when you need more space for long text, structured data or large result blocks.
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Copy buttons are available on generated output so results can be reused in code, documents or support chats.
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Most operations are deterministic: the same input and options produce the same output.
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For sensitive content, prefer local browser tools and review the result before sharing it further.
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