Pi Calculator: Simple and Fun Math Tool

What is the Pi Calculator?

This tool computes the number pi from different series. You can choose among several formulas. It shows approximations and compares them to a standard value.

How It Works

Step-by-Step Instructions

1. Pick one of the formulas from the drop-down menu. Options include the Leibniz Formula, Nilakantha Series, Wallis Product, and Machin's Formula.
2. Enter a number between 1 and 1,000,000. This sets the number of terms in the series.
3. Click the "Calculate Pi" button. The tool then runs the chosen formula.
4. Review the result. The calculated value, error, and accuracy are shown.
5. Watch the graph. It shows how the result gets closer to pi as you increase the terms.

Input Fields Explanation

The drop-down menu lets you choose which formula to use. A description is shown in a box. For example, the Leibniz series displays as "π/4 = 1 - 1/3 + 1/5 - 1/7 + ...".

The term field accepts a number from 1 to 1,000,000. Type your number there to decide how many terms the formula will sum.

Output Details

The output shows the calculated pi value. It also gives the actual pi (using JavaScript's Math.PI value). Accuracy is given in percent. The error is shown in exponential form.

A graph plots the result as the series builds up. This helps show how the computed value approaches pi.

Usage Tips and Considerations

• A higher term count gives a closer value to pi.
• Using a very high term count might slow down the calculation.
• Choose different formulas to compare how fast they come near the real value.

Common Use Cases

• Students exploring math series.
• Hobbyists testing mathematical ideas.
• Teachers showing practical math calculations in class.

Final Thoughts

This tool makes it easy to see how series can approximate pi. Follow the steps and play with the number of terms. You can compare various formulas. The graph adds a visual touch that makes learning fun. Enjoy experimenting with the Pi Calculator!