Powers, Square Roots & Nth Roots

Excel Formulas › Math

All versionsPOWERSQRT

Raising to a power uses POWER or the ^ operator; square roots use SQRT. The trick most people miss: any nth root is just a fractional exponent — the cube root of 27 is 27^(1/3).

Quick formula: to raise A2 to a power, or take its cube root:
=A2 ^ 3 // A2 cubed =A2 ^ (1/3) // cube root of A2
A whole-number exponent is a power; the reciprocal (1/n) is the nth root. POWER(A2, 3) equals A2^3.

Functions used (tap for the full reference guide):

POWERSQRT

The example

Powers and roots of a value.

AB
1OperationResult
22 ^ 101024
3SQRT(144)12
427 ^ (1/3)3

The formula

Cube and cube root:

=POWER(A2, 3) → A2 cubed =A2 ^ (1/3) → cube root of A2

How it works

Powers and roots are two sides of the same operation:

  1. A2 ^ n (or POWER(A2, n)) raises A2 to the power n — 2^10 = 1024.
  2. SQRT(A2) is the square root; it equals A2 ^ (1/2).
  3. Any nth root is a power of 1/n: the cube root is ^(1/3), the 4th root is ^(1/4).
  4. Negative exponents give reciprocals: 2^-1 = 0.5. Fractional exponents like 8^(2/3) combine a power and a root.

This powers CAGR and growth math: the per-period growth rate is (end/start)^(1/periods) - 1 — an nth root in disguise. Fractional exponents show up all over finance and science.

Try it: interactive demo

Live demo

Enter a value and an exponent (try 1/3 for cube root).

Result:

Variations

Square root

SQRT or ^(1/2):

=SQRT(144)

Any nth root

The 5th root of 32:

=32 ^ (1/5)

Compound growth rate

An nth root in finance:

=(end/start) ^ (1/years) - 1

Pitfalls & errors

#NUM! from roots of negatives. The square root of a negative (or an even root) isn’t a real number — SQRT(-4) errors. Use ABS or IMSQRT (complex) if needed.

Parenthesize fractional exponents. Write A2^(1/3), not A2^1/3 — without parentheses Excel computes (A2^1)/3.

Operator precedence. -2^2 is 4 in Excel (it negates after squaring? actually it’s 4) — when in doubt, add parentheses to make intent clear.

Practice workbook

📊
Download the free Powers, Square Roots & Nth Roots practice workbook
Powers and roots with live POWER/SQRT/fractional-exponent examples, the growth-rate variant, plus 4 challenges with answers. No sign-up required.

Frequently asked questions

How do I raise a number to a power in Excel?
Use the ^ operator or POWER: =A2^3 or =POWER(A2, 3) both cube A2.
How do I calculate an nth root in Excel?
Use a fractional exponent: the cube root is =A2^(1/3), the 5th root is =A2^(1/5). Always parenthesize the fraction.
Why does a root return #NUM!?
You're taking an even root (like a square root) of a negative number, which has no real result. Use ABS first or the complex-number IMSQRT.

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Related formulas: CAGR · Compound interest · Combinations & permutations

Function references: POWER · SQRT