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Sum of Squares Calculator

Compute the sum of squares for the first N integers, a range n₁..n₂ or a custom list, using the n(n+1)(2n+1)/6 formula with exact big-integer arithmetic.

Related tools

All Geometry tools →
Infinite Series Sum CalculatorTen classic families — geometric, p-series, telescoping, alternating harmonic, Leibniz, Basel, Σ1/n! — with their closed form (π²/6, ln 2, π/4, e), the convergence condition and the partial sums.Riemann Sum CalculatorApproximate a definite integral by left, right, midpoint, trapezoidal or Simpson sums, drawn against the curve with a per-interval table.Digit sum calculatorAdd up the digits of a number and find its digital root.Sum calculatorAdd up a list of numbers and get the total, count and average.Sum of cubes calculatorAdd up cubes fast: the sum of the first n cubes (1³+2³+…+n³, which equals the square of the n-th triangular number), the cubes over a range n₁³…n₂³, or the cubes of your own list of numbers. Exact integer arithmetic, however large.Sum of positive integers calculatorThe sum of all whole numbers from n₁ to n₂ in one step — Gauss's trick, n₂(n₂+1)/2 − (n₁−1)n₁/2, instead of adding them one by one. From 1 to 100 is the classic 5050; works for any range and any size.3D Distance CalculatorCompute the distance between two points in space, with an isometric view, the Δx / Δy / Δz components and the midpoint.Angle Bisector Calculator (triangle)Enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors.

Sum of Squares Calculator works straight from this page — free, instant, nothing to install. It sits under Geometry in our catalogue, alongside Infinite Series Sum Calculator and Riemann Sum Calculator.

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 Sum of Squares Calculator do?

Compute the sum of squares for the first N integers, a range n₁..n₂ or a custom list, using the n(n+1)(2n+1)/6 formula with exact big-integer arithmetic.

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 Sum of Squares Calculator different from Infinite Series Sum Calculator?

They sit next to each other but answer different questions. Infinite Series Sum Calculator: ten classic families — geometric, p-series, telescoping, alternating harmonic, Leibniz, Basel, Σ1/n! — with their closed form (π²/6, ln 2, π/4, e), the convergence condition and the partial sums. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Riemann Sum Calculator is the closest one after this: Approximate a definite integral by left, right, midpoint, trapezoidal or Simpson sums, drawn against the curve with a per-interval table.

What else is worth having open alongside it?

Digit sum calculator and Sum 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 →
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.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.