With a 50 mm lens at f/4, the aperture measures 50 ÷ 4 = 25/2 = 12.5 mm, and f/4 lets in 1/4 of the light of f/2. Shutter speed is a fraction of a second, and the f-number is a ratio between the lens’s focal length and the diameter of its aperture. With those two ideas you can work out how much light gets in and how to offset one setting with another.
Each step on the scale halves the time
A shutter speed is written as a fraction of a second: 1/250 s is one of the 250 equal parts a second is divided into. With the same numerator, the larger fraction is the one with the smaller denominator, so on the shutter scale a larger denominator means a shorter time. The English Wikipedia article Shutter speed lists the standard scale, from 1/1000 s up to 1 s, and notes that each step roughly doubles or halves the light (accessed October 17, 2026).
The names on the scale are rounded. If each step were exactly double the one before, the powers of 2 would give 1/64 and 1/128 where the camera shows 60 and 125. That is why two neighboring values on the scale do not have a ratio of exactly 2, and the calculation in the example shows it.
Worked example: comparing two neighboring speeds
You compare two photos taken at the same aperture, one at 1/60 s and one at 1/125 s. How many times longer was the first exposure?
- Order them. Both numerators are 1; since 60 is less than 125, 1/60 is the larger fraction.
- Divide. 1/60 ÷ 1/125 = 1/60 × 125/1 = 125/60.
- Simplify. The GCD of 125 and 60 is 5, and 125/60 = 25/12.
The first photo received 25/12 times the time of the second, that is, 2.0833… times.
Check: 2 × 60 = 120, which is a little less than 125. The ratio has to come out somewhat above 2, and 25/12 = 2.0833… does. Rounded to 2.08, the value is off by 1/300, because 25/12 − 2.08 = 1/300.
With the exact values 1/64 and 1/128 the ratio would be exactly 2. The gap between 2 and 2.0833… comes from the rounded name, not from the calculation. The compare fractions calculator orders two times, and divide fractions gives the ratio between them.
The f-number is a ratio between two lengths
The f-number is calculated as N = F ÷ D, where F is the focal length and D is the diameter of the aperture. The English Wikipedia article F-number defines it as the ratio of the system’s focal length to the diameter of the entrance pupil (accessed October 17, 2026). Solving for D gives D = F ÷ N, which is a division of fractions when F and N are not whole numbers.
With a 50 mm lens at f/4, the diameter is 50 ÷ 4 = 25/2 = 12.5 mm. At f/2 it is 25 mm, twice as much. With the same focal length, a larger f-number means a smaller diameter. The f-number has no unit, because it divides two lengths in the same unit: it is a ratio, and the ratio to fraction calculator writes it as a fraction.
Why f/4 lets in only a quarter of the light of f/2
The light that gets in is proportional to the area of the aperture, and the area grows with the square of the diameter. Going from f/2 to f/4, the diameter is cut in half, from 25 mm to 12.5 mm. The area drops to (1/2)², and so does the light.
The f-number series: each step multiplies by √2
The standard scale is f/1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, according to the same article. For each mark to let in half the light of the previous one, the area has to be divided by 2, and that is the same as dividing the diameter by √2, where √2 ≈ 1.4142, with error less than 0.0001. The printed values are rounded: 1.4 comes from √2, 2.8 from 2√2 ≈ 2.828 (error less than 0.001) and 5.6 from 4√2 ≈ 5.657 (error less than 0.001).
The table uses the theoretical values. The square of the f-number is proportional to 1/light, so dividing 4 by that square gives the light relative to f/2.
| f-number | Theoretical square | Light relative to f/2 |
|---|---|---|
| f/1.4 | 2 | 2 |
| f/2 | 4 | 1 |
| f/2.8 | 8 | 1/2 |
| f/4 | 16 | 1/4 |
| f/5.6 | 32 | 1/8 |
| f/8 | 64 | 1/16 |
| f/11 | 128 | 1/32 |
| f/16 | 256 | 1/64 |
Each row is half the one before it, and the powers of 2 in the square confirm it. The printed numbers only approximate the theoretical series, so two cameras can differ slightly in the actual light.
Time and aperture offset each other
The total light is proportional to the time divided by the square of the f-number. If the time is divided by 2 and the aperture is opened one step, the quotient does not change, because you lose half on one side and get it back on the other. The time goes from 1/500 s to 1/500 ÷ 2 = 1/1000 s, and the square of the f-number goes from 4 (f/2) to 2 (f/1.4).
| Time | f-number | Time ÷ (f-number)² |
|---|---|---|
| 1/125 s | f/4 | 1/2000 |
| 1/250 s | f/2.8 | 1/2000 |
| 1/500 s | f/2 | 1/2000 |
| 1/1000 s | f/1.4 | 1/2000 |
All four pairs give the same quotient, 1/2000, using the theoretical f values. With the printed numbers the match is approximate. Choosing one pair or another changes how the photo looks, since a short time freezes motion, and the aperture also changes the depth of field, an effect this light calculation does not measure.
Exercises with shutter speed and aperture
Practice
- A 100 mm lens is set to f/8. What is the diameter of the aperture?
- What fraction of the light of f/5.6 does f/11 let in?
- A photo turns out well at 1/500 s and f/4. If you stop down to f/5.6, what time keeps the same light?
See the answers
- 100 ÷ 8 = 25/2 = 12.5 mm.
- From f/5.6 to f/11 there are two steps, and two halves in a row give 1/4.
- Closing one step splits the light in half, so the time doubles: 1/500 × 2 = 1/250 s.
To review the operations used here, multiply fractions covers products of halves, fraction powers explains why (1/2)² is 1/4, and drawing fractions shows area as a part of a whole.
Sources
- English Wikipedia, article “Shutter speed,” accessed October 17, 2026.
- English Wikipedia, article “F-number,” accessed October 17, 2026.
- Both articles were consulted for the shutter scale and for the definition of the f-number; the rest is calculation with fractions.