String Around a Circle Calculator
Solve the rope around the Earth problem: find the uniform gap from extra string, or the extra length needed for a desired gap.
Uniform gap
0.15915 m
15.92 cm — the original object size does not affect this gap.
Circle measurements
- Original radius
- 6,371 km
- New radius
- 6,371.000159 km
- Original diameter
- 12,742 km
- New diameter
- 12,742.000318 km
- Original circumference
- 40,030.17 km
- New circumference
- 40,030.175 km
- Increase in diameter
- 31.83 cm
Gap enlarged for visibility — diagram not to scale.
Same extra length, same gap
Add the same amount of string around a basketball or around Earth, and the gap will be exactly the same. The object’s size does not matter—only the extra string length does. Here, 1 m of extra string creates a 15.92 cm gap.
Illustrative circle sizes — not to scale.
How the string around a circle formula works
The original circumference is C = 2πr. Adding length L makes the new radius (C + L) ÷ 2π. Subtracting the original radius gives L ÷ 2π, so the object radius cancels completely.
For the classic string around the Earth puzzle, use Earth’s approximate radius of 6,371 km and add 1 m. Adding 1 meter of string creates a uniform gap of about 0.15915 meters, or 15.92 centimeters, everywhere around the equator.
For a sphere such as Earth, the rope follows one great circle, such as the equator. It does not cover the spherical surface.
Assumptions
- The cross-section is a perfect circle and the string remains centered.
- The gap is uniform around the entire circle.
- String thickness, stretching, gravity, and sagging are ignored.