Skip to content
ENExplore Calculators

Cube Root By Hand Calculator

Work out cube root by hand instantly with clear inputs, formula shown and shareable results.

About Cube Root By Hand Calculator

Newton's method applied to x³ − v = 0 gives the iteration x ← x − (x³ − v)/(3x²). Unlike square roots, cube roots exist for negative numbers, so the sign is carried through.

Formula

Newton iteration

xₖ₊₁ = xₖ − (xₖ³ − v) / (3xₖ²)

Worked example

With the default values below, Cube Root By Hand Calculator returns Cube root of 17.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number
4,913
Newton iterations to showaccepts 1–20
5

Results

Cube root
17.00000000
Newton's method estimate
215.68199510
Integer part of the root
17
Remainder after the integer part
0.000000

Step by step

  1. 1Values used
  2. 2Newton iteration
  3. 3Cube root= 17.00000000
  4. 4Newton's method estimate= 215.68199510
  5. 5Integer part of the root= 17
  6. 6Remainder after the integer part= 0.000000

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is ∛4913?

Exactly 17, since 17³ = 4913.

Can I take the cube root of a negative number?

Yes. ∛(−27) = −3, because a negative cubed is negative.

Related Calculators

Cube Root By Hand Calculator – Calculate Cube root