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Digital Root Calculator

Compute the additive and multiplicative digital root of any number in base 2, 8, 10 or 16, with the full chain, the mod-9 shortcut and the persistence count.

Related tools

All Algebra & equations tools →
Rational Root Theorem CalculatorEvery ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.Nth root calculatorCompute any root (square, cube, nth) of a number.Cube root calculatorCompute the cube root of a number, plus its cube.Primitive root calculatorFind the primitive roots modulo n — the generators g whose powers g¹, g², … run through every number coprime to n before repeating (order equal to φ(n)). Primitive roots exist only when n is 1, 2, 4, pᵏ or 2pᵏ for an odd prime p; the tool reports the smallest one, the exact count φ(φ(n)) and lists them. They are the backbone of discrete-logarithm cryptography and Diffie–Hellman key exchange.Square root calculatorCompute the square root of a number, plus its square.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.Absolute Value Equation SolverSolve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.Absolute Value Inequality SolverSolve absolute-value inequalities such as |x+3| < 5 or |x−2| > 3 and get the solution as an interval, with AND/OR reasoning explained step by step.

Digital Root Calculator works straight from this page — free, instant, nothing to install. You will find it under Algebra & equations, with Rational Root Theorem Calculator and Nth root calculator for the neighbouring cases.

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 is Digital Root Calculator?

Compute the additive and multiplicative digital root of any number in base 2, 8, 10 or 16, with the full chain, the mod-9 shortcut and the persistence count.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Digital Root Calculator different from Rational Root Theorem Calculator?

They sit next to each other but answer different questions: Rational Root Theorem Calculator is the one to open when you need it to every ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Nth root calculator is the closest one after this: Compute any root (square, cube, nth) of a number.

What else is worth having open alongside it?

Cube root calculator and Primitive root calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.How-toHow to Find the Area of a Triangle: Base × Height and Heron's FormulaTwo reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.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.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.