FractaleriaFree tool
String art nail spacing calculator
Enter the diameter of the circle and how many nails you want: it tells you how far apart they go, every how many degrees, and which skips you can string.
- Distance between nails
- — in a straight line, with the compass
- Angle between nails
- — with the protractor
- Along the circle
- — measured on the curve
- Suggested board
- —
Number:
How it is calculated
- The straight-line distance between two neighboring nails is the diameter multiplied by the sine of 180° divided by the number of nails.
- The angle between one nail and the next is 360° divided by the number of nails.
- To mark them without a protractor, set the compass to that distance and walk around the circle, mark by mark. If you end up a little over or short when you close the loop, spread the difference out.
How many nails to use
In Fractalería designs the nails sit between 1 and 5 cm apart (about 3/8 in to 2 in). Under 6 mm (1/4 in) it gets hard to hammer and pass the string; with more spacing the pattern is more open and faster to string. More nails give finer curves, but also more hours of work.
Why prime numbers matter
When you string by counting, you always advance the same number of nails. If the total number of nails is prime, any skip passes through all of them before coming back to the start. If it is not, only the skips that share no divisor with the total close completely; the others form a star or a polygon and leave nails unused.
Common measurements
| Diameter | Nails | Distance | Angle |
|---|---|---|---|
| 20 cm | 12 | 5.2 cm | 30° |
| 20 cm | 18 | 3.5 cm | 20° |
| 20 cm | 24 | 2.6 cm | 15° |
| 20 cm | 36 | 1.7 cm | 10° |
| 20 cm | 48 | 1.3 cm | 7.5° |
| 20 cm | 60 | 1 cm | 6° |
| 24 cm | 12 | 6.2 cm | 30° |
| 24 cm | 18 | 4.2 cm | 20° |
| 24 cm | 24 | 3.1 cm | 15° |
| 24 cm | 36 | 2.1 cm | 10° |
| 24 cm | 48 | 1.6 cm | 7.5° |
| 24 cm | 60 | 1.3 cm | 6° |
| 34 cm | 12 | 8.8 cm | 30° |
| 34 cm | 18 | 5.9 cm | 20° |
| 34 cm | 24 | 4.4 cm | 15° |
| 34 cm | 36 | 3 cm | 10° |
| 34 cm | 48 | 2.2 cm | 7.5° |
| 34 cm | 60 | 1.8 cm | 6° |
| 54 cm | 12 | 14 cm | 30° |
| 54 cm | 18 | 9.4 cm | 20° |
| 54 cm | 24 | 7 cm | 15° |
| 54 cm | 36 | 4.7 cm | 10° |
| 54 cm | 48 | 3.5 cm | 7.5° |
| 54 cm | 60 | 2.8 cm | 6° |
From the numbers to the template
The generator does this calculation for you, draws the mandala with its layers of string and gives you the nail template as a PDF at actual size.
Frequently asked questions
How many nails does a 30 cm (12 in) circle take?
It depends on the spacing you want: at 2 cm between nails it is about 47; at 3 cm, about 31.
How do I mark the nails without a protractor?
Set the compass to the straight-line distance the calculator gives you and walk around the circle marking each point. If you end up a little over or short at the end, spread the difference among all of them.
Does it work for squares or hexagons?
This calculator is for circles. The free design mode of the generator also spaces the nails on triangles, squares, pentagons, hexagons and octagons.