Advanced Regula Falsi Calculator

Enter bounds, tolerance, and iterations for robust solving. Review approximations with error tracking and charts. Export clean reports for homework, verification, and decision support.

This tool applies the false position method to estimate a root of a nonlinear equation using a bracketing interval, detailed iteration output, accuracy controls, exports, and a function graph.

Calculator Inputs

Function f(x)

Use explicit multiplication like 4*x. Supported functions: sin, cos, tan, sqrt, abs, exp, log, log10.

Lower Bound (xl)

Upper Bound (xu)

Approx. Error Tolerance (%)

Function Tolerance |f(xr)|

Maximum Iterations

Decimal Places

Reset

Example Data Table

Function	Lower Bound	Upper Bound	Error Tolerance (%)	Function Tolerance	Approximate Root
x^3 + 4*x^2 - 10	1	2	0.001	0.000001	1.36523
cos(x) - x	0	1	0.001	0.000001	0.73909
exp(-x) - x	0	1	0.001	0.000001	0.56714

Formula Used

Regula Falsi estimate:
xr = (xl * f(xu) - xu * f(xl)) / (f(xu) - f(xl))

Approximate relative error:
ea = |(xr,new - xr,old) / xr,new| × 100

Interval update rule:
If f(xl) * f(xr) < 0, the root remains in [xl, xr].
If f(xl) * f(xr) > 0, the root remains in [xr, xu].
If f(xr) = 0, the exact root has been found.

How to Use This Calculator

Enter a valid function in terms of x.
Provide lower and upper bounds that bracket a root.
Set the approximate error tolerance and function tolerance.
Choose the maximum number of iterations and display precision.
Press Calculate Root to view the result, table, and graph.
Use the export buttons to save the data as CSV or PDF.

Frequently Asked Questions

1) What is the Regula Falsi method?

It is a bracketing root-finding method. It draws a straight line through two points on the function and uses the x-axis intercept as the next approximation.

2) When should I use this method?

Use it when you know a root lies between two values and the function changes sign across that interval. It is especially useful for nonlinear equations.

3) Why must the interval bracket a root?

The method depends on opposite signs at the endpoints. Without a sign change, the algorithm cannot guarantee that a root lies inside the interval.

4) What does the approximate error mean?

It measures how much the newest estimate differs from the previous one. Smaller values usually mean the method is stabilizing near the root.

5) Why include a function tolerance too?

A small approximate error alone may not guarantee that the function value is close to zero. Function tolerance adds a second convergence check.

6) Which functions can I type?

You can use expressions such as x^3-4*x+1, sin(x), exp(-x)-x, sqrt(x)-2, and log(x)-1.

7) Why can convergence be slow sometimes?

Regula Falsi may keep one endpoint fixed for many iterations. That can slow progress when the function shape is unbalanced near the root.

8) What do the CSV and PDF downloads contain?

The CSV file stores the numerical iteration data. The PDF export summarizes the result and includes the iteration table for reporting or review.