False Position Method Calculator – Interactive Root Finding Tool

What is the False Position Method?

The False Position Method (or Regula Falsi) is a numerical method used to find the roots of a continuous function. Similar to the Bisection Method, it requires the function to change signs over an interval, but instead of using the midpoint, it uses a linear approximation to find the next point.

Learn more about how it works

1. Start with an interval [a, b] where f(a) and f(b) have opposite signs.
2. Use the formula \( c = \frac{a f(b) - b f(a)}{f(b) - f(a)} \) to calculate the next approximation.
3. Evaluate f(c).
4. If f(c) is close enough to 0, c is the root.
5. If f(c) has the same sign as f(a), update a = c. Otherwise, update b = c.
6. Repeat steps 2-5 until the desired accuracy is achieved or the maximum number of iterations is reached.

Input Parameters

Try these:

x³ - x - 10

x² - 4

sin(x) - 0.5x

log(x) - 1

e^x - 2

x⁴ - 16

cos(x) - x

x³ + 3x² - 1

Function (in terms of x):

Interval Start (a):

Interval End (b):

Iterations:

Steps & Output

How to Read the Table

This table shows the iterative steps of the False Position Method:

• Iteration: The current step number.
• a: The left endpoint of the interval.
• b: The right endpoint of the interval.
• c: The next approximation using the formula.
• f(a): The function value at a.
• f(b): The function value at b.
• f(c): The function value at the new approximation c.

Iteration	a	b	c (Approximation)	f(a)	f(b)	f(c)

Function Graph

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