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Magic square generator

Generate a magic square of any order from 3 to 20 — a grid of the numbers 1…N² where every row, column and diagonal adds to the same magic constant. It picks the right construction automatically: the Siamese method for odd orders, diagonal complements for multiples of four, and the Strachey method otherwise.

Related tools

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Square diagonal calculatorCompute the diagonal and area of a square from its side length.Square calculatorAll four measures of a square from any one. Give the side, the area, the perimeter or the diagonal and it returns the rest — side s, area s², perimeter 4s and diagonal s√2 — instantly.Chi-Square Test Calculatorχ² test of independence on any contingency table, showing observed, expected, the contribution and the standardised residual of every cell, plus Cramér's V. Cells with an expected count below 5 are flagged, because that is when the test stops being valid.Completing the Square CalculatorRewrite ax² + bx + c into vertex form a(x − h)² + k, with the vertex, the completed-square steps and the real or complex roots.Root Mean Square CalculatorRMS shown next to the plain mean, because on signed data the mean collapses to nearly zero while the RMS holds the magnitude that actually matters. Also gives the crest factor, the sum of squares and each value's share of it.Square numbers listGenerate a list of perfect squares — n² for consecutive integers from any starting point. Choose how many and where to begin, and it returns the squares and their sum with exact big-integer arithmetic, handy for spotting patterns and differences.Square root calculatorCompute the square root of a number, plus its square.3D Distance CalculatorCompute the distance between two points in space, with an isometric view, the Δx / Δy / Δz components and the midpoint.

Open Magic square generator and you get an answer straight away, with no account to create. Its place is under Geometry; Square diagonal calculator and Square calculator answer the questions closest to this one.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Magic square generator do?

Generate a magic square of any order from 3 to 20 — a grid of the numbers 1…N² where every row, column and diagonal adds to the same magic constant. It picks the right construction automatically: the Siamese method for odd orders, diagonal complements for multiples of four, and the Strachey method otherwise.

What does a concrete case look like?

3 × 3 → Σ = 15 — the tool shows every step in between, not just the final figure.

When would I actually use this?

Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.

What is the most common mistake?

Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.

How is Magic square generator different from Square diagonal calculator?

They sit next to each other but answer different questions. Square diagonal calculator: compute the diagonal and area of a square from its side length. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Square calculator is the closest one after this: All four measures of a square from any one. Give the side, the area, the perimeter or the diagonal and it returns the rest — side s, area s², perimeter 4s and diagonal s√2 — instantly.

What else is worth having open alongside it?

Chi-Square Test Calculator and Completing the Square Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The formulas are the classical ones and the results are exact to the precision shown — geometry does not change with the year or the country, so nothing here needs updating.

Further reading

All guides →
How-toHow to Calculate the Square Metres of a RoomFind a room's area by multiplying length by width. Here's the method for rectangular, L-shaped and round rooms, and why area drives your material orders.ExplainerA Cone Is Exactly One Third of Its CylinderRadius 5, height 10: the cone holds 261.8 and the cylinder around it holds 785.4. The ratio is exactly a third, and it holds for any base shape at all.ExplainerOne Formula That Is Also a Rectangle and Also a TriangleParallel sides of 8 and 5 with a height of 4 give an area of 26 — the average width times the height. Make the two sides equal and it is a rectangle; shrink one to nothing and it is a triangle.ExplainerTwice as Wide Holds Four Times as Much; Twice as Tall Holds TwiceA cylinder of radius 5 and height 10 holds 785.4 units of volume. Double the radius and it holds 3,141.6; double the height instead and it holds 1,570.8.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.