String Girdling Earth Calculator
The string girdling Earth calculator can help you determine the extra string length needed to achieve a desired gap or the resulting gap achieved by splicing a given string length.
Gap per unit of extra string
| Length added | Gap |
|---|---|
| 1 | 0.159155 |
| 2 | 0.31831 |
| 5 | 0.795775 |
| 10 | 1.591549 |
| 100 | 15.915494 |
The formulas
adding L to a circumference lifts it by L / 2π
Why the answer surprises everyone
Tie a string tight around the Earth’s equator, then add just one metre. The string now sits about 16 cm off the ground — all the way round.
The reason is that C = 2πr is linear: Δr = ΔC / 2π. The original size cancels out entirely, so one metre added to a tennis ball lifts it by the same 16 cm. Intuition fails here because we expect a proportional effect, and there isn’t one.
Everything follows from the radius
A circle has one degree of freedom, so any single measurement fixes all the others:
d = 2rC = 2πr = πdA = πr² = πd²/4 = C²/4π
Going backwards, r = C/2π and r = √(A/π). The calculator above accepts whichever you happen to have.
Area grows with the square
Double the radius and the circumference doubles, but the area quadruples. That is why a 16-inch pizza is more than twice the food of a an 11-inch one, and why pipe capacity rises so sharply with bore.