Vesica Piscis
Make the vesica piscis symbol at an exact size: two circles of the same radius, each passing through the other’s centre, and the lens where they overlap. Start from one of our 15 designs: two circles, the lens filled, the two equilateral triangles, a ratio sheet that prints the lens height, width, area and outline for your size, the lens alone (mandorla), an upright version, a chain of three or four circles, a colouring page, a tracing sheet, five compass construction steps, a stencil or a sheet of small lenses. Set the circle radius in inches or centimetres on US Letter or A4 and download a PDF, 300 DPI PNG or SVG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size). Each circle passes through the other’s centre, so the lens is √3 × r tall and r wide (√3 : 1 = 1.7321 : 1).
Vesica piscis
Lines and colours
Size and paper
Runs in your browser with our own code: nothing you choose is uploaded or saved. The drawings are our own. You may use what you make here, including commercially, with no credit needed.
How to make and print a vesica piscis
- Pick a design: two circles, lens, triangles, ratio sheet, mandorla, chain, steps or stencil.
- Turn the circles, lens fill, triangles, height and width lines, points and letters on or off.
- Set the circle radius (r) in inches or cm; the lens is √3 × r tall and r wide.
- For a stencil, set the bridge width between the cut-outs.
- Download the PDF and print at 100% (Actual size); check the 1 in (or 2 cm) bar.
What you can use it for
- Learning the first compass construction in geometry
- Geometry lessons on equilateral triangles and √3
- Logo, arch and window layouts at the √3 : 1 ratio
- Colouring and tracing sheets
- Cutting a stencil or vinyl from the SVG
- A starting grid for patterns of overlapping circles
The 15 vesica piscis designs
| Design | Circles | Direction | Shown | Layout |
|---|---|---|---|---|
| Vesica piscis: two circles | 2 | Side by side | circles | One figure |
| Lens filled | 2 | Side by side | circles, lens fill | One figure |
| With the two equilateral triangles | 2 | Side by side | circles, triangles, letters | One figure |
| Ratio sheet: √3 : 1 with measurements | 2 | Side by side | circles, triangles, height / width, letters, ratio panel | One figure |
| Height and width lines | 2 | Side by side | circles, lens fill, height / width | One figure |
| Upright (one circle above the other) | 2 | Upright | circles, lens fill | One figure |
| Lens alone (mandorla outline) | 2 | Side by side | lens fill | One figure |
| Chain of 3 circles (2 lenses) | 3 | Side by side | circles, lens fill | One figure |
| Chain of 4 circles (3 lenses) | 4 | Side by side | circles, lens fill | One figure |
| Colouring page: bold outlines | 2 | Side by side | circles | One figure |
| Tracing sheet: light grey lines | 2 | Side by side | circles, triangles | One figure |
| Gold on navy | 2 | Side by side | circles, lens fill | One figure |
| Construction steps (Euclid I.1) | 2 | Side by side | circles | Construction steps |
| Stencil: lens and two crescents, 2 mm bridges | 2 | Side by side | circles | Stencil |
| Sheet of small lenses (0.6 in radius) | 2 | Side by side | circles, lens fill | Sheet of small figures |
All are our own drawings. Each design is a starting point: change any part, the colours, line width, radius and paper.
Vesica piscis measurements
| Measurement | In units of the radius r |
|---|---|
| Distance between the centres (AB) | 1 r |
| Lens height (CD) | 1.7321 r (√3 r) |
| Lens width | 1 r |
| Height : width | 1.7321 : 1 (√3 : 1) |
| Triangle sides (ABC, ABD) | 1 r (equilateral) |
| Each lens edge | 120° arc of one circle |
| Lens area | 1.2284 r² ((2π/3 − √3/2) r²) |
| Lens outline | 4.1888 r ((4π/3) r) |
| Whole figure | 3 r wide, 2 r tall |
Our tests check the height, width and triangle sides to a trillionth of the radius, and the area and outline against numeric integration.
Measurements for common sizes
| Circle radius r | Lens height | Lens width | Lens area | Lens outline |
|---|---|---|---|---|
| 1 in | 43.9941 mm | 25.4 mm | 792.495 mm² | 106.3953 mm |
| 2 in | 87.9882 mm | 50.8 mm | 3169.98 mm² | 212.7905 mm |
| 5 cm | 86.6025 mm | 50 mm | 3070.9242 mm² | 209.4395 mm |
| 10 cm | 173.2051 mm | 100 mm | 12283.697 mm² | 418.879 mm |
Construction steps
| Step | What you draw |
|---|---|
| 1 | Draw a circle of radius r round point A. Keep the compass at this setting. |
| 2 | Mark B anywhere on the circle and draw a circle round B: it passes through A. |
| 3 | Mark C and D where the two circles cross: the lens between them is the vesica piscis. |
| 4 | Join A, B and C, and A, B and D: two equilateral triangles with sides r (Euclid, Elements I.1). |
| 5 | Draw CD (the lens height, 1.732 × r) and the line through A and B (the width AB = r). |
Each step adds to the one before and the last step is the whole figure; earlier lines print grey and the new ones dark.
Chains of circles
| Circles | Lenses | Width | Points marked | Largest radius, US Letter |
|---|---|---|---|---|
| 2 | 1 | 3 r | 4 | 2.5 in |
| 3 | 2 | 4 r | 7 | 1.875 in |
| 4 | 3 | 5 r | 10 | 1.5 in |
| 5 | 4 | 6 r | 13 | 1.25 in |
Sizes
| Paper | Largest radius, portrait | Largest radius, landscape | Largest radius, portrait (cm) |
|---|---|---|---|
| US Letter | 2.5 in | 3.316 in | 6.35 cm |
| A4 | 2.422 in | 3.2 in | 6.15 cm |
| Bridge | Smallest radius, seed of life | Smallest radius, vesica piscis |
|---|---|---|
| 1 mm | 3.7321 mm | 1 mm |
| 2 mm | 7.4641 mm | 2 mm |
| 3 mm | 11.1962 mm | 3 mm |
| 5 mm | 18.6603 mm | 5 mm |
History
The vesica piscis appears in the first proposition of Euclid’s Elements, as the first step in building an equilateral triangle on a given line (source: Wikipedia, Vesica piscis, read 12-Nov-2026). This page is about the geometry only: we make no claims about meanings, energy or health.
Which tool to use
| You want | Use |
|---|---|
| Two circles and the √3 : 1 lens | Vesica Piscis |
| Seven circles and the six-petal rosette | Seed of Life |
| The 19-circle flower and larger grids | Flower of Life |
| The golden ratio (1.618 : 1) instead of √3 : 1 | Golden Ratio Calculator |
For other proportions, use the Golden Ratio Calculator; to measure the 60° angles, the Online Protractor; for a triangle grid, the Isometric Graph Paper.
What prints
| Download | What is in it |
|---|---|
| The page at real size, vector: circles, petals, lines, points and labels, with a 1 in (or 2 cm) check bar | |
| PNG 300 DPI | The page as a picture |
| SVG | The page at real size, with fills, circles, lines, ring and points in separate groups (for cutting machines and drawing programs) |
More free tools
Drawing with a compass?
Geometry and pattern tools that run privately in your browser, with no sign-up and no watermark.
Frequently asked questions
What is a vesica piscis?
The lens-shaped overlap of two circles of the same size, each drawn through the other’s centre. The name is Latin for the bladder of a fish; the lens on its own is also called a mandorla, Italian for almond (source: Wikipedia, Vesica piscis, read 12-Nov-2026).
What is the vesica piscis ratio?
The lens is √3 times as tall as it is wide: with circles of radius r, its height is √3 × r (about 1.7321 r) and its width is r. The tool works these out for your radius and the ratio sheet prints them.
Why √3?
The two centres and either crossing make an equilateral triangle with sides r. Its height is √3 / 2 × r, and the lens height is two of those heights, so √3 × r.
How do I draw it with a compass?
Draw a circle round a point A and keep the compass at that setting. Mark a point B on the circle and draw a circle round B: it passes through A. The two crossings are C and D. Joining A, B and C gives an equilateral triangle; this is the first proposition of Euclid’s Elements.
What are its area and outline?
With radius r the lens area is (2π/3 − √3/2) r², about 1.2284 r², and its outline is (4π/3) r, about 4.1888 r, because each edge is a 120° arc. Our tests check both against a numeric measurement.
What is the chain of circles?
Three or more circles in a row, each through its neighbour’s centre. Each pair makes its own vesica piscis, so n circles give n − 1 lenses.
How does the stencil work?
The lens and the two crescents either side of it are the cut-outs. Each is shrunk by half the bridge width, so the strip between them is at least the bridge you set and no piece is cut loose.
Is anything uploaded?
No. The figure is drawn by JavaScript in your browser. Nothing you choose is sent anywhere or saved when you close the page.
Is it free?
Yes. There is no sign-up, no watermark and no limit.