Glance at the summary firstThe summary from the end of the lesson, as a road map before you start reading.
The golden ratio is a ratio of about 1.618 that divides a line at the 0.618 point; the ratio of consecutive numbers of the Fibonacci sequence gradually approaches it. In photography it gives, as the phi grid, lines a little closer to the center than the rule of thirds grid, and as the golden spiral, a template that carries the gaze along a curving path to a point; but most of the claims stretching from temples to shells don't hold up when measured. This useful but not magic helper line works when light and expression are built right; the eye you put on the intersection point being readable on every skin decides more than the line itself.
Learning goal
You will be able to explain what the golden ratio is, through its number and the way it divides a line, and see how this ratio is carried into photography as a helper line. You will calculate that the phi grid differs from the rule of thirds grid only by lines a little closer to the center; you will try how the golden spiral can be used to lead the gaze along a curving path to a point; you will recognize how the Fibonacci sequence approaches this ratio; and you will tell apart which of the claims loaded onto the golden ratio are measurable and which are myth; you will also know what you need to look at so that an eye you place on an intersection point is really readable, on every skin.
The question
You open a frame you took in a ceramics workshop in an editing program. Wet clay turning on the potter's wheel, spiral marks left by fingers on the clay, bowls waiting to dry lined up on shelves at the back. When you pick the crop tool, a grid comes up on the screen and a few options appear in the menu: a thirds grid, a phi grid, and a strange drawing that divides the screen into ever smaller squares with a spiral curling through it.
A few days ago someone on the internet wrote that this spiral was the secret of great photographers, and that the same number was hidden everywhere in nature and art. Is the golden ratio a secret or a myth? In this lesson we will talk about what this number is, what it really gives the photographer, and where the stories that have grown around it break away from measurement.
Context
These lines in the crop tool come from mathematics. Imagine dividing a line into two parts so that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part. This way of dividing was defined in ancient Greek geometry, in Euclid's book called the Elements. The adjective "golden" was attached to it much later, and over time the number settled at the center of many claims about art, architecture and nature.
In Lesson 6.3 we saw the rule of thirds, which divides the frame into nine equal boxes. The golden ratio is a close relative of it: both suggest placing the main subject a little away from the exact middle. Seeing how small the difference between them is, is the first step to giving the golden ratio its proper weight.
Simple explanation
What is the golden ratio?
The golden ratio is a number of about 1.618, and is usually written with the Greek letter phi. When you divide a line by this ratio, the larger part takes about sixty-one point eight percent of the whole, and the smaller part thirty-eight point two percent; that is, the dividing point sits at about 0.618 of the line. A rectangle whose sides are in this ratio is called a golden rectangle. When you cut a square the size of its short side from this rectangle, the part left over is again a golden rectangle, and this process can be continued forever.
This ratio is also closely related to a sequence of numbers. The Fibonacci sequence is the sequence in which each number is the sum of the two numbers before it: 1, 1, 2, 3, 5, 8, 13, 21 and so on. The ratio of two consecutive numbers in the sequence gradually approaches the golden ratio: the ratio of 8 to 5 is 1.6, and the ratio of 21 to 13 is about 1.615. The number of spirals formed by the seeds in a sunflower head often matches numbers in this sequence; this is a plant growth pattern that has been measured and confirmed.
How does the phi grid differ from the rule of thirds?
The rule of thirds grid cuts the frame at its one-third and two-thirds points. The phi grid, on the other hand, puts its lines at about the thirty-eight percent and sixty-two percent points. In a frame 6000 pixels wide, the vertical lines of the rule of thirds stand at the 2000th and 4000th pixels; the lines of the phi grid are at about the 2292nd and 3708th pixels. That is, the phi lines are a few hundred pixels closer to the center than the thirds lines.
During shooting, this difference is usually as small as sliding a step to the side or turning the camera a few degrees. In practice, both grids point to the same region, an area a little away from the center but not reaching the edge. The phi grid offers a slightly more gathered placement for those wary of pushing the subject too far toward the edge; the thirds grid, on the other hand, is found more often on camera screens because it is easy to calculate. Which one is more effective depends on the subject and on the rest of the frame.
What is the golden spiral for?
The curve joining the corners of the squares cut one after another from inside a golden rectangle gives the drawing known as the golden spiral. When you put this spiral over the frame in the crop tool, the point where the spiral curls most tightly suggests a place for focus; the spiral's wide arm, on the other hand, carries the gaze along a path curving from the edge of the frame toward this point. With lines that are already curved, like a river bend, a staircase or the finger marks on the clay, this helper drawing can be useful.
You need to know two of its limits. The spiral can be turned in four different directions and mirrored; in many frames, one of these is bound to match something. Also, most cameras' frames are in a 3:2 or 4:3 ratio; this comes to 1.5 or 1.33, not 1.618. When the spiral is fitted to such a frame, it is stretched and is no longer a true golden spiral. Using the spiral not as a measure, but as a template that helps your eye notice a curving path, is a more honest approach.
Where does the myth begin?
It is often written that the golden ratio is hidden everywhere, in ancient temples, famous paintings, seashells and the human face. A significant share of these claims don't hold up when measured: when enough lines are drawn over a building or a painting, one of these lines is bound to give a ratio close to 1.618. Many seashells really do grow in the shape of a spiral, but when measured, most of these spirals don't fit the golden ratio exactly. Whether people prefer the golden rectangle over other rectangles was tested by experiments for a long time, and the results didn't agree with each other.
For the photographer, the conclusion is simple: the golden ratio is a placement suggestion like the rule of thirds; it doesn't make a photograph strong on its own, and doesn't make a photograph that doesn't fit it weak. Light, the moment, expression and the balance of weights we saw in Lesson 14.7 decide much more than exactly where a line falls. A useful helper line, but not magic.
Visual evidence
You go back to the workshop. The potter is a dark-skinned, middle-aged woman who has tied her hair back with a cloth; her hands, wet with clay, are on the wheel. You open the golden spiral in the crop tool and turn it: the spiral's wide arm curls from the bottom right corner of the frame along the curved marks of the turning clay, and its tightest point comes to the woman's eye looking at the clay. When you crop the same frame with the phi grid, you put the eye near the horizontal thirty-eight percent line; with the thirds grid, on the one-third line; on the screen, the difference between the two crops is the width of a finger.
But in the first frame, even though the end of the spiral falls exactly on the eye, the eye is the weakest place in the frame: when the woman bends her head to the clay, the area under her eyebrows has stayed dark, there is no glint in the eye, and the intersection point sits like an empty shadow. You ask her permission and request that she turn the wheel a little toward the window beside it; the window light now comes to her face from the side. In the next frame there is a small, bright reflection of the window inside her eye, and her eyelashes and the line of her lips can be made out. The line is in the same place; what really filled the point was the light.
Common mistakes
Common mistakeThinking the golden ratio is the formula for a photograph's success.
Fitting a frame to the spiral doesn't save weak light or an empty moment. The fix: look first at light, moment and balance, and use the grid as the last adjustment.
Common mistakeFinding a golden ratio in every frame by turning and mirroring the spiral, and counting this as proof.
With enough lines, everything matches something. The fix: use the spiral as a helper only if there is already a curving line in the frame.
Common mistakeNot checking whether the face placed on the intersection point is readable.
An eye placed in the right spot but left in shadow leaves the point empty. The fix: turn the person a little toward the light, and check on the screen that there is a glint and detail in the eye, on every skin.
Summary
The golden ratio is a ratio of about 1.618 that divides a line at the 0.618 point; the ratio of consecutive numbers of the Fibonacci sequence gradually approaches it. In photography it gives, as the phi grid, lines a little closer to the center than the rule of thirds grid, and as the golden spiral, a template that carries the gaze along a curving path to a point; but most of the claims stretching from temples to shells don't hold up when measured. This useful but not magic helper line works when light and expression are built right; the eye you put on the intersection point being readable on every skin decides more than the line itself.
Mini assignment
In this assignment you will crop the same frame with different grids and measure the difference with your own eye.
- Photograph a scene with a curving line, a road, a staircase or a fold of fabric.
- Crop the frame in an editing program first with the thirds grid, then with the phi grid, and put the two crops side by side.
- Place the golden spiral template on the same frame in four directions, and note which one follows a real curve in the frame and which ones only happen to match something by chance.
- In a portrait, place the eye on an intersection point and look at whether there is a glint and detail in the eye; if not, turn the person to the light and shoot again.
Check yourself
- Did the difference between the thirds and phi crops really change the photograph's effect, or was it only a shift of a few hundred pixels?
- Which of the spiral placements relied on a real line in the frame?
- Does the eye on the intersection point carry a glint and detail, regardless of skin tone?
Glossary
| Term | Short definition |
|---|---|
| Golden ratio | The ratio, of about 1.618, in which the ratio of the whole to the larger part equals the ratio of the larger part to the smaller. |
| Golden rectangle | A rectangle whose long side is to its short side as the golden ratio. |
| Phi grid | Helper lines that divide the frame at about the 38 percent and 62 percent points, a little closer to the center than the thirds grid. |
| Golden spiral | A curve passing through the squares cut one after another from a golden rectangle, used as a placement template in cropping. |
| Fibonacci sequence | A sequence in which each number is the sum of the two before it, and whose consecutive ratios approach the golden ratio. |
Mini quiz
1. The golden ratio is roughly equal to which number?
- A) 1.333
- B) 1.5
- C) 1.618
- D) 2
2. Where are the lines of the phi grid compared with the thirds grid?
- A) Closer to the edges
- B) A little closer to the center
- C) In the exact center
- D) In the same place
3. What happens when a golden spiral is placed on a 3:2 frame?
- A) The spiral is stretched, because the frame's ratio is 1.5, not 1.618
- B) The spiral fits exactly
- C) The spiral shrinks by itself
- D) The frame turns into a golden rectangle
4. If the end of the golden spiral falls exactly on an eye but the eye has stayed in shadow, without a glint and without detail, what helps most?
- A) Turn the spiral to match another point
- B) Turn the person a little toward the light and check that there is a glint and detail in the eye
- C) Crop the frame again with the thirds grid
- D) Nothing; because the point is in the right place, the frame is strong
Answers
- C — The golden ratio is about 1.618; 1.5 is the 3:2 frame ratio.
- B — The phi lines are at about 38 and 62 percent, the thirds lines at 33 and 67 percent; the phi lines are a little closer to the center.
- A — Because the frame isn't in a 1.618 ratio, the spiral is stretched as it is fitted to it.
- B — The intersection point is only a place; what makes that point readable is the light falling on the eye.
Summary card
- Golden ratio ≈ 1.618; it divides a line at the 0.618 point; Fibonacci ratios approach it.
- Phi grid: about 38 and 62 percent; a little closer to the center than the thirds grid.
- Golden spiral: a template that links a curving path to a point; stretched in a 3:2 frame.
- Most claims don't hold up when measured: a useful helper line, not magic.
- Light fills the eye at the intersection; look for a glint and detail on every skin.
Bridge to the next lesson
Imagine photographing a frame of the potter in the workshop without fitting any grid, from the exact middle of the turning clay, symmetrically; maybe that frame looks stronger than all the frames that fit the helper lines. After learning the rule of thirds, the phi grid, balance and the other placement suggestions, when and why does it make sense to move away from them? The next lesson talks about breaking the rules of composition, and what separates a mistake from a choice.