Edge Length Calculator
The edge of a cube, a square, or any regular polygon is the length of one of its sides, and it is the single number every other measurement follows from: volume, surface area, area, and perimeter all derive from it. This edge length calculator works backwards from whichever measurement you already have.
Choose the shape, tell the tool which value you know (volume, surface area, area, perimeter, diagonal, circumradius, or a diagonal variant), enter the number, and get the edge length to four decimal places with the exact formula it used. Six shapes and fifteen input paths are covered on this one page.
Quick Answer
A cube with a volume of 512 has an edge length of 8.0000 units, because the edge is the cube root of the volume. The same tool works from what you have instead: a square with a diagonal of 14 has an edge of 9.8995 units, and a regular tetrahedron with a volume of 25.4558 has an edge of 6.0000 units.
Key takeaways
- Edge length is the master measurement of a regular shape: once you have it, volume, area, surface area and diagonals all follow.
- Fifteen paths lead to it on this page, including two most tools skip: a cube from its face diagonal and a square from its circumradius.
- The formula used is printed with every result, so each answer can be checked by hand in one line.
- Every shape here is regular, with all edges equal. An irregular box or a scalene triangle has no single edge length to find.
- Quick Answer
- How to use the edge length calculator
- All fifteen formulas, with a checked example for each
- Worked examples: three shapes, three different starting points
- What other edge length calculators miss
- Where edge length gets used
- Units, precision and the regular-shape limit
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the edge length calculator
Three choices and one number. The results stay hidden until you click Calculate, so you can change the shape or the known value and re-run freely.
- Shape: pick the cube, square, equilateral triangle, regular hexagon, regular octagon or regular tetrahedron you are working with.
- I know the: pick which measurement you already have. The list rebuilds for each shape, so you only ever see paths that exist.
- Known value: type the measurement as a plain number. Keep units consistent: a volume in cubic centimeters returns an edge in centimeters.
- Calculate: the edge length appears to four decimal places with the exact rearranged formula that produced it. Copy or share the result with the buttons under it.
All fifteen formulas, with a checked example for each
Every path in the tool is one standard geometry relation with a, the edge length, made the subject. The cube relations come from V = a³, S = 6a² and the two diagonals a√2 (across a face) and a√3 (through the solid), the same properties set out in the MathWorld entry on the cube. The polygon relations come from each shape's area and perimeter formulas, and the tetrahedron path from V = a³ ÷ (6√2).
| Shape | Known | Formula | Example |
|---|---|---|---|
| Cube | Volume | a = V^(1/3) | 512 → 8.0000 |
| Cube | Surface area | a = sqrt(S / 6) | 150 → 5.0000 |
| Cube | Space diagonal | a = d / sqrt(3) | 17.3205 → 10.0000 |
| Cube | Face diagonal | a = f / sqrt(2) | 14.1421 → 10.0000 |
| Square | Area | a = sqrt(A) | 100 → 10.0000 |
| Square | Perimeter | a = P / 4 | 40 → 10.0000 |
| Square | Diagonal | a = d / sqrt(2) | 14 → 9.8995 |
| Square | Circumradius | a = sqrt(2) x rc | 7 → 9.8995 |
| Equilateral triangle | Area | a = sqrt(4A / sqrt(3)) | 43.3013 → 10.0000 |
| Equilateral triangle | Perimeter | a = P / 3 | 30 → 10.0000 |
| Regular hexagon | Area | a = sqrt(2A / (3 x sqrt(3))) | 10.3923 → 2.0000 |
| Regular hexagon | Perimeter | a = P / 6 | 24 → 4.0000 |
| Regular octagon | Area | a = sqrt(A / (2 x (1 + sqrt(2)))) | 100 → 4.5509 |
| Regular octagon | Perimeter | a = P / 8 | 40 → 5.0000 |
| Regular tetrahedron | Volume | a = cbrt(12V / sqrt(2)) | 25.4558 → 6.0000 |
Two of these paths deserve a note. The square's circumradius (the radius of the circle passing through all four corners) is half the diagonal, so the edge is the circumradius times sqrt(2). The tetrahedron constant looks arbitrary until you expand it: its volume is a³√2 ÷ 12, and cbrt(12V ÷ sqrt(2)) is that relation turned around, as the MathWorld entry on the regular tetrahedron confirms with V = a³ ÷ (6√2), the same thing written differently.
Worked examples: three shapes, three different starting points
Each example below was run through the tool's own code, not worked out separately, so the numbers you see are the numbers the calculator returns.
Cube from volume: a storage box holds 512 cubic units. The edge is the cube root of 512, which is 8.0000 units. This is the pre-filled example: select Cube and Volume, leave 512 in the box, and click Calculate. Cube roots of awkward volumes are the slow part by hand, which is why a cube root calculator is the natural companion tool for checking this path.
Square from diagonal: a square tile measures 14 units corner to corner. Its edge is 14 ÷ sqrt(2) = 9.8995 units. Diagonal problems like this one are Pythagoras in disguise: the diagonal is the hypotenuse of the right triangle formed by two edges, and tools built around diagonal distance solve the forward version of the same relation.
Tetrahedron from volume: a regular tetrahedron holds 25.4558 cubic units. Its edge is cbrt(12 x 25.4558 ÷ sqrt(2)) = cbrt(216) = 6.0000 units. Once you have that edge, the four triangular faces follow at once, because each face is an equilateral triangle of the same edge.
What other edge length calculators miss
The current top results are narrow. Checked against the leading tools for this keyword, the pattern is consistent.
- Cube only: the most common edge length tools handle a cube from its volume, surface area and space diagonal, then stop. A square, hexagon or tetrahedron question sends you to a different site.
- One formula per page: the big formula libraries split every rearrangement onto its own page, one for a square from its diagonal, another for a cupola from its surface-to-volume ratio, each wrapped in its own ads and layout.
- No face diagonal, no circumradius: the two less obvious paths, a cube from the diagonal of one face and a square from the radius of its circumscribed circle, are missing from the single-shape tools entirely.
- Answers without workings: most tools return a number and nothing else. Here the exact rearranged formula is printed under every result, so a student can copy the method, not just the answer.
This page covers all of their ground plus more: six shapes, fifteen input paths, one consistent interface.
Where edge length gets used
Working backwards to an edge is a design move: you know the capacity, coverage or span you need, and the edge is the dimension you can actually cut, order or draw.
- Packaging: a carton that must hold a set volume starts as a cube root. From the edge, the cube surface area calculator gives the board area the carton will consume.
- Fencing and framing: a fixed perimeter divided by 4, 6 or 8 gives the panel or rail length for a square, hexagonal or octagonal layout before anything is bought.
- Crystal and unit-cell work: lattice volumes are cube volumes, so the volume path returns the cell edge that diffraction data is reported against.
- Homework and checking: the printed formula under each result makes the tool usable as a marking aid: the method is visible, so a wrong answer can be traced to the step that slipped.
Units, precision and the regular-shape limit
The calculator is unit-agnostic, but your inputs cannot mix units. An area must be in square units of the same system as the edge you expect out: enter a surface area in square inches and the edge comes back in inches. The classic slip is entering a volume measured in cubic centimeters and reading the edge as meters.
Results are shown to four decimal places. The underlying arithmetic keeps full floating-point precision, and only the display is rounded, so chaining the rounded edge into a second calculation can cost you a little accuracy: for precision work, re-derive from the original measurement instead.
The honest limit is regularity. Every formula here assumes all edges are equal, which is true by definition for a cube, a square, an equilateral triangle, a regular hexagon, a regular octagon and a regular tetrahedron. A rectangular box has three different edges and needs its own volume relation for each; no single edge length exists to find.
Disclaimer: This is a geometry reference tool. The formulas are standard textbook relations, but dimensions for engineering, construction, or manufacturing should always be verified against authoritative references and professional drawings before cutting material or placing orders.
Frequently Asked Questions
For flat polygons the words mean the same thing. For solid shapes, an edge is the line segment where two faces meet, and a regular solid has all edges equal, which is what this calculator finds.
Divide the space diagonal by sqrt(3): a = d / sqrt(3). A space diagonal of 17.3205 units gives an edge of 10.0000 units. Use the Cube / Space diagonal mode.
Divide the face diagonal by sqrt(2): a = f / sqrt(2). A face diagonal of 14.1421 units gives an edge of 10.0000 units, and the calculator has a dedicated Cube / Face diagonal mode for it.
Yes: multiply the circumradius by sqrt(2), so a = sqrt(2) x rc. A circumradius of 7 units gives an edge of 9.8995 units. Use the Square / Circumradius mode.
Any consistent unit: centimeters, meters, inches, or plain abstract units. The result comes back in the same unit you entered, because the formulas only relate lengths, areas, and volumes to each other.
Four decimals are precise enough for design, homework, and workshop use while staying readable. The calculation itself uses full floating-point precision and only rounds for display.
Because only a regular shape has a single edge length. A cube, square, equilateral triangle, regular hexagon, regular octagon and regular tetrahedron have all edges equal, so one number describes every side. An irregular shape has different sides, and each one needs its own relation.
Add This Calculator to Your Website
Embed this calculator on your own site with the code below. Pick a size to preview it live, then copy the code.
Powered by Calculator Zilo
References
- Weisstein, Eric W. Cube, MathWorld, a Wolfram Resource. Accessed October 21, 2026.
- Weisstein, Eric W. Regular Tetrahedron, MathWorld, a Wolfram Resource. Accessed October 21, 2026.
- Weisstein, Eric W. Hexagon, MathWorld, a Wolfram Resource. Accessed October 21, 2026.
- Weisstein, Eric W. Octagon, MathWorld, a Wolfram Resource. Accessed October 21, 2026.
- Weisstein, Eric W. Square, MathWorld, a Wolfram Resource. Accessed October 21, 2026.
- Math Is Fun. Cube (Hexahedron). Accessed October 21, 2026.