Monte Carlo Estimator: Estimating π and Beyond
July 7, 2025
Monte Carlo methods have always fascinated me especially the idea that randomness can be harnessed to estimate something as fundamental as π. So I decided to build a Monte Carlo Estimator in C++ to see this concept in action.
This was a simple but eye-opening project that deepened my understanding of probability, convergence, and the elegance of using simulation to solve problems that look purely theoretical on paper.
🎯 What the Program Does
Here’s the basic idea:
- Randomly generate points inside a square.
- Check whether each point falls within a unit circle centered at the origin.
- Estimate π using the formula:
π ≈ 4 × (points in circle / total points) - Repeat this process thousands (or millions) of times.
- Display the results as the approximation gets closer to the real value.
It’s almost magical watching randomness settle into predictability.
🧠 What I Learned
1. Randomness in Practice
I dug into how C++ generates random numbers with rand() and srand(). Even though they’re fairly basic, they were perfect for demonstrating the core idea behind Monte Carlo simulations.
2. Geometric Probability
This project reinforced how geometry and probability intersect. The fact that you can approximate π by throwing darts at a virtual square is one of the most elegant examples of applied math I’ve seen.
3. Balancing Accuracy and Performance
I experimented with different iteration counts to see how quickly the estimates converged. More samples definitely mean better accuracy, but they also mean longer runtime, which was an interesting tradeoff to observe firsthand.
4. Visualizing Progress in the Console
I added print statements to show the estimation improving over time. Watching the number stabilize closer and closer to 3.14159 made the learning feel real and tangible.
📷 Screenshot
📂 Tech Stack
- C++
- Math & Geometry
- Terminal-Based UI
🔗 Links
It’s easy to underestimate small projects like this, but they can teach you a lot. This Monte Carlo Estimator wasn’t just a way to practice C++ it was a reminder that sometimes the simplest ideas can reveal the most about how math and programming work together.
If you’re curious about Monte Carlo methods or just want to see the code in action, check out the repo or drop me a message, I’d love to hear your thoughts.
— Maruf