What is the golden ratio?

The golden ratio (phi, approximately 1.618) is a proportion often used in design and typography because two segments in that ratio are considered visually balanced.

UtilitiesReady to use

Golden Ratio Calculator

Calculate the complementary dimension of a layout using the golden ratio, approximately 1.618.

Guide

Interactive workspace

No account required

Golden Ratio Calculator

Known dimensionDecimal placesUnits (optional)

Larger segment (a)

161.80

Larger segment (a): 161.80
Smaller segment (b): 100.00
Total (a + b): 261.80

Check: a ÷ b = 1.6180 ≈ φ (1.6180), and (a + b) ÷ a = 1.6180.

Show golden rectangle and spiral

Golden rectangle

Known sideThat side is the

The other side is 61.80; the rectangle is 100.00 × 61.80 with area 6180.34.

Fibonacci approximation

Highlight n = 20

F(20) = 6,765, F(21) = 10,946, ratio 1.61803400 — off from φ by 9.77e-9.

n	F(n)	F(n+1)	F(n+1) ÷ F(n)	Error vs φ
2	1	2	2.00000000	3.82e-1
3	2	3	1.50000000	1.18e-1
4	3	5	1.66666667	4.86e-2
5	5	8	1.60000000	1.80e-2
6	8	13	1.62500000	6.97e-3
7	13	21	1.61538462	2.65e-3
8	21	34	1.61904762	1.01e-3
9	34	55	1.61764706	3.87e-4
10	55	89	1.61818182	1.48e-4
11	89	144	1.61797753	5.65e-5
12	144	233	1.61805556	2.16e-5
13	233	377	1.61802575	8.24e-6
14	377	610	1.61803714	3.15e-6
15	610	987	1.61803279	1.20e-6
16	987	1,597	1.61803445	4.59e-7
17	1,597	2,584	1.61803381	1.75e-7
18	2,584	4,181	1.61803406	6.70e-8
19	4,181	6,765	1.61803396	2.56e-8
20	6,765	10,946	1.61803400	9.77e-9
21	10,946	17,711	1.61803399	3.73e-9
22	17,711	28,657	1.61803399	1.43e-9
23	28,657	46,368	1.61803399	5.45e-10
24	46,368	75,025	1.61803399	2.08e-10
25	75,025	121,393	1.61803399	7.95e-11
26	121,393	196,418	1.61803399	3.03e-11
27	196,418	317,811	1.61803399	1.16e-11
28	317,811	514,229	1.61803399	4.43e-12
29	514,229	832,040	1.61803399	1.69e-12
30	832,040	1,346,269	1.61803399	6.46e-13
31	1,346,269	2,178,309	1.61803399	2.47e-13
32	2,178,309	3,524,578	1.61803399	9.41e-14
33	3,524,578	5,702,887	1.61803399	3.60e-14
34	5,702,887	9,227,465	1.61803399	1.38e-14
35	9,227,465	14,930,352	1.61803399	5.33e-15
36	14,930,352	24,157,817	1.61803399	2.00e-15
37	24,157,817	39,088,169	1.61803399	8.88e-16
38	39,088,169	63,245,986	1.61803399	2.22e-16
39	63,245,986	102,334,155	1.61803399	2.22e-16
40	102,334,155	165,580,141	1.61803399	0.00e+0
41	165,580,141	267,914,296	1.61803399	0.00e+0
42	267,914,296	433,494,437	1.61803399	0.00e+0
43	433,494,437	701,408,733	1.61803399	0.00e+0
44	701,408,733	1,134,903,170	1.61803399	0.00e+0
45	1,134,903,170	1,836,311,903	1.61803399	0.00e+0
46	1,836,311,903	2,971,215,073	1.61803399	0.00e+0
47	2,971,215,073	4,807,526,976	1.61803399	0.00e+0
48	4,807,526,976	7,778,742,049	1.61803399	0.00e+0
49	7,778,742,049	12,586,269,025	1.61803399	0.00e+0
50	12,586,269,025	20,365,011,074	1.61803399	0.00e+0
51	20,365,011,074	32,951,280,099	1.61803399	0.00e+0
52	32,951,280,099	53,316,291,173	1.61803399	0.00e+0
53	53,316,291,173	86,267,571,272	1.61803399	0.00e+0
54	86,267,571,272	139,583,862,445	1.61803399	0.00e+0
55	139,583,862,445	225,851,433,717	1.61803399	0.00e+0
56	225,851,433,717	365,435,296,162	1.61803399	0.00e+0
57	365,435,296,162	591,286,729,879	1.61803399	0.00e+0
58	591,286,729,879	956,722,026,041	1.61803399	0.00e+0
59	956,722,026,041	1,548,008,755,920	1.61803399	0.00e+0
60	1,548,008,755,920	2,504,730,781,961	1.61803399	0.00e+0

Ratios of consecutive Fibonacci numbers converge to φ; by n = 20 the error is already below one part in a hundred thousand.

Design outputs

Container width (px)Gap (px)

Main column 726.81 px (61.8%) · Sidebar 449.19 px (38.2%), after the 24 px gap.

.golden-layout {
  display: grid;
  grid-template-columns: 1.618fr 1fr;
  gap: 24px;
}

Spacing scale base (px)

:root {
  --space-xs: 6.11px;
  --space-sm: 9.89px;
  --space-md: 16.00px;
  --space-lg: 25.89px;
  --space-xl: 41.89px;
  --space-2xl: 67.78px;
  --space-3xl: 109.67px;
}

The golden ratio (φ) is approximately 1.618, a proportion often used in design layouts and compositions.

How to use it

Enter the known positive dimension.
Choose whether it is the larger or smaller segment.
Read the complementary dimension and check that the same unit is used throughout.

What is Golden Ratio Calculator?

Calculate the complementary dimension of a layout using the golden ratio, approximately 1.618.

How it works

SiteIndex multiplies or divides your known dimension by the golden ratio (approximately 1.618) to calculate the complementary segment used in golden-ratio based layouts.

Common uses

Find a complementary column width using golden ratio proportions.
Design a layout section that follows classic golden ratio composition.
Check the paired dimension for a golden-ratio-based crop or grid.

Limitations

This calculates a mathematical proportion, not a usability or visual-quality guarantee. It does not edit an image.

Frequently asked questions

What is the golden ratio?: The golden ratio (phi, approximately 1.618) is a proportion often used in design and typography because two segments in that ratio are considered visually balanced.

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