Cube Root Calculator

Compute ∛x for any real number—plus √x and x³—with live results, adjustable precision, quick examples, recent history, and a short number-line view.

Quick examples:

Number x (for ∛x)

Cube root is defined for all real numbers. Results update as you type.

Decimal places

Scientific notation when very large/small

Enter a valid number for an instant result, use Calculate, or tap a quick example.

Prefer only square roots? Try the dedicated square root calculator.

What is a cube root?

The cube root of a number x is the value y such that y × y × y = x. We write y = ∛x. For example, ∛8 = 2 because 2³ = 8, and ∛27 = 3 because 3³ = 27. Unlike square roots, every real number has a real cube root: ∛(−8) = −2 because (−2)³ = −8. Cube roots appear when reversing volume formulas (side length from volume of a cube), in algebra when solving x³ = k, and in scaling laws where quantities grow with the third power.

How to calculate cube root manually?

For perfect cubes, factor the radicand into primes and group each prime in triples—each triple contributes one factor outside the root. Example: 216 = 2³ × 3³, so ∛216 = 2 × 3 = 6. For decimals or non-cubes, use Newton's method on f(y) = y³ − x: repeatedly replace y with y − (y³ − x)/(3y²) until the value stabilizes, or use logarithms: ∛x = sign(x) · e^((ln|x|)/3) for x ≠ 0. This calculator uses optimized Math.cbrt for speed and accuracy.

Cube root table (1–100)

Reference values for ∛n where n is a whole number from 1 to 100. Perfect cubes (1, 8, 27, 64) show exact integers; other entries are shown to six decimal places.

Cube roots from 1 through 100
n	∛n
1	1
2	1.259921
3	1.442250
4	1.587401
5	1.709976
6	1.817121
7	1.912931
8	2
9	2.080084
10	2.154435
11	2.223980
12	2.289428
13	2.351335
14	2.410142
15	2.466212
16	2.519842
17	2.571282
18	2.620741
19	2.668402
20	2.714418
21	2.758924
22	2.802039
23	2.843867
24	2.884499
25	2.924018
26	2.962496
27	3
28	3.036589
29	3.072317
30	3.107233
31	3.141381
32	3.174802
33	3.207534
34	3.239612
35	3.271066
36	3.301927
37	3.332222
38	3.361975
39	3.391211
40	3.419952
41	3.448217
42	3.476027
43	3.503398
44	3.530348
45	3.556893
46	3.583048
47	3.608826
48	3.634241
49	3.659306
50	3.684031
51	3.708430
52	3.732511
53	3.756286
54	3.779763
55	3.802952
56	3.825862
57	3.848501
58	3.870877
59	3.892996
60	3.914868
61	3.936497
62	3.957892
63	3.979057
64	4
65	4.020726
66	4.041240
67	4.061548
68	4.081655
69	4.101566
70	4.121285
71	4.140818
72	4.160168
73	4.179339
74	4.198336
75	4.217163
76	4.235824
77	4.254321
78	4.272659
79	4.290840
80	4.308869
81	4.326749
82	4.344481
83	4.362071
84	4.379519
85	4.396830
86	4.414005
87	4.431048
88	4.447960
89	4.464745
90	4.481405
91	4.497941
92	4.514357
93	4.530655
94	4.546836
95	4.562903
96	4.578857
97	4.594701
98	4.610436
99	4.626065
100	4.641589

FAQs

What is the cube root of a negative number?: The cube root of a negative number is negative. For example, ∛(−27) = −3 because (−3)³ = −27. Unlike square roots, cube roots are defined for every real number.
Is ∛x the same as x^(1/3)?: For real x, yes: raising x to the one-third power gives the real cube root. The calculator uses Math.cbrt, which correctly handles negatives (unlike some naive power formulas).
Why does ∛2 show a long decimal?: 2 is not a perfect cube, so its cube root is irrational—it cannot be expressed as a fraction. The value shown is a high-precision decimal approximation; choose 2–10 decimal places above.
How accurate is this calculator?: Results use double-precision floating point (IEEE-754). You control display precision from 2 to 10 decimals; toggle scientific notation for very large or small magnitudes.