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As of 2024, humans have calculated 105 trillion digits of π. But how many do we really need?

• Everyday use: 3.14 is enough.
• Engineering: 3.1416 is usually plenty.
• ISRO/NASA: about 15 digits

What if we measure the biggest thing with the tiniest ruler?

The largest thing that humans can measure is the circumference of observable-universe, whose radius is

R ≈ 46.5 \text{billion light-years} ≈ 4.399\times10^{26} \text{m}

giving the circumference

C=2\pi R\approx2.764\times10^{27} \text{m}

The Planck length is considered the smallest physically meaningful unit of length, beyond it, space and time may not even make sense.

\ell_P\approx1.616255\times10^{-35} \text{m}

So, relative precision

\ell_P/C\approx5.85\times10^{-63}

That is 63 decimal digits.

Beyond that, the extra digits are pure poetry — infinite whispers of mathematics.

Links:
• Observable Universe: https://en.wikipedia.org/wiki/Observable_universe
• Plank: https://en.wikipedia.org/wiki/Planck_units
• Random pi: https://gsama.cc/guess-pi/