When you are new and starting off with photography one phrase that you are almost guaranteed to hear very soon is “f-stop”. Yes, I know it sounds weird and scary. Especially more so when you do not even know what it means. But don’t worry so much; today we are going to put this issue at rest, once and for all.

Before taking off though I would like to tell you that this article is intended for photographers and filmmakers who have at least the basic understanding of the three pillars of photography. Namely Aperture, Shutter Speed and ISO. If you are a beginner, I highly suggest you read the following pieces before you continue with this. It would make absolutely no sense to you if you do not know the fundamental principals working behind.

So what are we waiting for? Let’s begin…

Just a last thing, once you are absolutely through with f-stops and f-numbers, I will explain the T-stops which by then should be a cakewalk for you.

Resume >>

## F-Number

*F-number, f-stop, focal ratio they all denote a simple ratio between the focal length of the lens and the effective aperture. *

Now you may ask me that why on earth do you need to know about some strange maths problem?

First of all, the concept of f-numbers is not hard at all but extremely simple to understand. Secondly, you need to know about it so that you can communicate with your camera and with other fellow photographers about photography.

F-number in the simplest possible way is a **unit** which photographer use to measure light.

Not knowing about the f-number in photography is similar to going out shopping for groceries without having any idea how money is measured/calculated. Say if you need 10 items, each costing 5bucks, you would need 50bucks to get everything on the list right? Now if there is no unit (Indian rupee, US dollar, Euro etc) for money defined, how are you going to communicate with the store cashier? How is he going to tell you the price? And how much are you even going to pay? ……..You get it now?

F-number is the way photographers talk about light. I will explain more in just a bit.

## Calculation

F-number is calculated by just dividing the focal length of the lens by the diameter of the effective aperture. The focal length is nothing but the one embossed on your lens. Say if you have a 50mm prime lens. 50mm is the focal length of the lens. The effective aperture is the opening inside the lens which allows the light to pass through it into the camera.

So, f-number = Focal Length Of The Lens/Diameter Of The Effective Aperture.

Let me give you an example to drive this home.

Say you have a lens which has a focal length of 100mm and the diameter of the aperture inside the lens is 25mm. Then using the formula above you can easily calculate that the f-number, in this case, is f/4 (100 divided by 25). When we mention f-number, the standard way of representing it is f/#.

Now tell me that wasn’t easy!

## Unit Of Light

Like I mentioned before, f-number in photography is primarily used as a * relative* unit of light. The word relative has a pretty huge implication here. It means that a certain f-number does NOT always mean a certain amount of light. I know, I know this is a shock. Just keep going…

As you already know, light is nothing but an electromagnetic radiation, made up of tiny particles called photons. For the purposes of this example and the rest of the article, let us suppose we can measure light using the number of photons.

Circling back to the example now.

## Absolute Units

In science, most of the units we use are what we know as absolute units. These absolute units do NOT change and are fixed. For example, if I say the distance between point A and B is 5 kilometers. We immediately understand that the distance between point A and B is 5 times that of a kilometer. In this case, we use an absolute unit to define the distance, kilometer. One kilometer is a distance that is standardized and does not change with respect to time, geographical location, temperature or any other such thing. Its value is fixed, unconditionally.

Similarly, if I say, I bought a gallon of oil today. You would know that I bought a certain quantity of oil that is predefined. Yes, you can use different units to essentially mean the same amount of oil but they all will be actually the same thing. I could have just said I bought 3.785 liters of oil, and that would have meant exactly the same amount.

An absolute unit is one which is predefined and does not change with respect to anything.

## Relative Unit

Relative units are those whose **values change with respect to the values they are compared with. **For example, if I say, The Photon Tower is the tallest building in Kolkata, I just mean that no other building in Kolkata is as tall as the Photon Tower. It might just be the case that all the buildings in Kolkata is a one-storied building and the Photon Tower is just two stories.

The point being, you do not have an actual value when I say a statement like “The Photon Tower is the tallest building in Kolkata”. All the buildings in Kolkata and the Photon Tower could be anything, of any height. All we know is that the Photon Tower is the highest in the vicinity of the city. The unit which we use here is *relative, a*s compared to the other. And they change as the thing they are compared to changes.

## F-Number Is A Relative Unit

Earlier I gave you an example where I showed you how a lens of focal length 100mm and an effective aperture opening of 25mm gets us an f-number of f/4. Now what I want you to observe carefully is this number, f/4.

You see you can arrive at this number using a myriad of ways.

F-number = Focal Length/Diameter of the effective aperture= 100/25 = 400/100 = 60/15 = 16/4 = f/4

Do you see it now?

All that matters to keep the f-stop consistent is to **keep** the **ratio constant**. It never matters what the numbers involved are as long as they produce the same ratio. In other words, a 600mm lens and a 100mm lens both of which have a f-number, f/4, do not have the same size effective aperture opening. The 600mm lens would require an opening of 150mm and the 100mm lens would need just a 25mm opening, to have the same f-number value.

Let’s now bring this knowledge into the practical sphere.

## Concept Of Shutter Speed

The end result of knowing all the maths behind the numbers and values such as Aperture, Shutter Speed and ISO is to be able to expose the image….properly! Whether you take an ordinary everyday image, a panorama or a long exposure, as a photographer all you are trying to do while shuffling through the settings is to correctly expose your image.

Now imagine, like I asked you before, that you can see light is made up of tiny particles called photons and we can count them. Since we are already in a fantasy world, also imagine that these photons travel in a uniform straight line.

Ready?

To expose an image properly we need a stipulated amount of photons to reach the image sensor of the camera. Let us assume for an image, we need 50 such photons. The shutter speed of the camera is one of the easiest ways to understand the inner mechanics of the camera. It is exactly the same principle as a water tap and a bucket.

Say you can fill a bucket of water using a tap at your home in two minutes. So in four minutes, you can fill two buckets and in 10 minutes you could fill five. Correct? The shutter speed works identically like this. It is like a tap that you could open and close. The duration for which you keep it open determines the amount of photon you let in.

Continuing our hypothetical example. If we could see photon with our eyes and count them, we would see double the number of photons collected on the image sensor each time the shutter speed is doubled. So, if keeping the shutter open for 1 second allows 25 photons to come in, keeping it open for 2 seconds will allow 50 photons to enter. And voila! with 50 photons gathered on the image sensor, we will have a perfectly exposed image.

Seriously what could be easier than this?

## Concept Of An Aperture

This would need some surgery. Aperture values in photography are measured in f-stops. They look something like this:

Again a weird set of numbers up your street…This too has a reason.

Unlike the simpleton shutter speed where you can just double or halve the duration to double or reduce the amount of light, aperture does NOT function with a factor of ‘2’. This means that you just cannot multiply the last aperture value by 2 and expect a doubling of the light.

First and foremost, the f-numbers used to denote the size of the aperture are fractions and NOT perfect numbers. So in fact, **as you increase the f-number the aperture size decreases**. A f/1.4 aperture is a much larger opening than a f/16. To understand it even better I seriously urge you to read: Camera Aperture | A Comprehensive Guide For Beginners.

The aperture values indeed follow an approx 1.414 factor rather than 2. To know why this happens study this pdf which would explain the math behind this. If you don’t need the math, however, just know that by multiplying the last aperture size with approx 1.414 we can ensure the doubling of the photons which reach the image sensor.

I know this part is a bit confusing. It would take some time to both understand and feel this properly.

## How Constant F-Stop Numbers Mean Varying Aperture Sizes

A few years after I bought my new camera with a kit lens which had a floating aperture value, I so envied people with fixed aperture lenses. Especially Canon and Nikon’s 70-200 f/2.8 lenses. They were my dream (unfortunately they still are).

If you understood the little trick of math that I just used a while back to prove that a certain f-number could be produced in many ways, you should get this too!

Did you though?…..No?…Okay…here it is.

Let’s take the 70-200mm lens with a constant aperture of f/2.8. To have an aperture value of f/2.8 at the focal length 70mm, the diameter of the effective aperture has to be 25mm (70mm/2.8). However, at the maximum focal length of the same lens, to have an aperture of f/2.8, the opening needs to approximately 72mm in diameter.

Have a look at this again:

F-number = Focal Length/Diameter of the effective aperture= 70/25 = 200/72 = f/2.8.

In simple terms, for any zoom lens which has a fixed aperture, **the diameter of the effective aperture has to increase to compensate for the increase in a focal length** to keep the aperture value constant. As ironical as it may sound. The cheap kit lenses which are mostly bundled with many camera bodies and have a variable aperture are actually the ones which have a fixed size effective opening throughout the focal range of the lens for a specific f-number. It is precisely because the diameter remains the same while the focal length increases, that the f-number rises.

*But How Come The Exposure Doesn’t Change?*

It seems like a very plausible question to ask right about now. If the amount of light entering the camera depends on the **area **of the entrance pupil (effective aperture) and if that area increases, shouldn’t the exposure be affected?

In our earlier example of a 70-200mm lens if the diameter changes from an initial 25mm to 72mm (over 70mm to 200mm focal range), which also naturally increases the area of the opening, shouldn’t the amount of incoming light also increase?

Actually, it does.

Simply doubling the diameter of the entrance pupil lets in four times the amount of light in. While zooming in from 70mm (25mm diameter) to 140mm(50mm diameter), the amount of light actually increases four times. But what you also have to take into account is that the 140mm focal length projects each object in the lens’s field of view, twice the size in length and breadth. Effectively covering four times the area of the projection cast by the lens at 70mm. The illuminance value on the image sensor remains the same. The exposure, therefore, remains unhindered.

The concept of illuminance is very similar to that of density. Think of it that way.

## T-Stop

Yeah, the elephant in the room, T-stops.

The letter “T” stands for Transmission. Transmission of light through the lens barrel onto the sensor. Now that you have a pretty good understanding about f-stops, this should be as easy as pie.

*T-stops are f-stops corrected for absorbance and reflectance. * Since you like formulas so much (said no one ever).

T-stops = F-stop/Lens Transmittance%

For our example, at 70mm if the lens transmits 92% of the light, the effective T-stop would be approximately ‘3’ (2.8/92%). T-stops in effect determine the exposure of the image while f-stops determine the blur/bokeh/depth of field.

Let that sink in a bit.

## Difference Between F and T-Stops

F-stops are what we call theoretical values and T-stops actual values.

Story size example time.

At the beginning of a month, let’s suppose you make a monthly budget for yourself. Include everything there is. Rent, utilities, fuel, food, car, mortgage, party, going-out, cable, subscriptions etc. At the end of the month, if you compare. Do you really think your planned monthly budget will exactly fit your actual expenditures? I don’t think so. Yeah, sure some item which has no variability like rent and your monthly EMI for your phone wouldn’t. But other expenses like fuel, going out, party, etc would definitely be a little off. It is hard to predict these type of expenses since they are not standardized.

This is exactly the difference between f and T-stops. The f-stops are theoretically calculated values which simply do not take into account the type of material used to pass the light through. It’s glass alright for all lenses but NOT of the same kind. The only thing f-stops tell you is the amount of light that **should have** reached the sensor if there were absolutely nothing in between. NO, not even air.

But clearly, that cannot be the case. There need to be some lens elements, some glass optics.

These pieces of glass used to make the lens is what causes the projected f-numbers to go off a bit. Depending on their quality and how much light they absorb or reflect back, the amount of actual light reaching the all-important sensor changes. This value corrected for the minute changes caused by the lens elements is actually the T-stop.

Since no lens can ever have a perfect transmittance value of 100%. By definition for any particular lens, the f-stop will always be greater than the T-stop.

## Why It Doesn’t Really Matter

In the world of photography, you really wouldn’t see T-stops used in many places. Nearly all lenses currently sold have the f-number printed on the front and center but not the T-stops. In the video/filmmaking sphere, however, all you WILL see are T-stops. There are three simple reasons for this apparent discrimination.

- Photography is a one-shot deal. As a viewer you only see a single image at a time, there is no continuity. Films are however totally continuous. From this very reason stems the need to monitor exposure more accurately. If the exposure varies even a little from one frame to the other in a film, the entire sequence would seem jagged and unnatural. Photography simply doesn’t have this problem.
- Although the f and T-stops vary in almost all cases, the offset is generally not very much. So, even if you underexpose or overexpose an image owing to the difference in the values, you wouldn’t be very far off. A little post-processing ( which probably you would do anyway) will very easily fix it.
- Unless you are using an external light meter and relying on just the meter in your camera, it also has the capability to adjust. Most modern day cameras have TTL (Through The Lens) metering system. This means that the camera only meters the amount of light that enters the camera having passed through the lens. So in case you are using any of the semi or fully automatic mode (please DON’T), the camera can seamlessly adjust to the minute difference thereby exposing the image correctly.
- It is expensive to conduct tests to figure out the exact T-stop of a lens. Since the f-stops are theoretical, you can just calculate them off a spec sheet. But for T-stops, you would have to conduct an actual test. These tests are indeed very costly and time-consuming. Naturally, for an everyday consumer-level lens, manufacturers skip it completely and advertise the lens with the f-number only.

## Conclusion

I would hence very definitely advise you as always, to concentrate more on the “Art” side of photography than the “Tech”. I am not saying that it is not important but that it is only useful to help you make the art you want. Think of them as tools and nothing more. Your vision and your perspective that you want to illustrate on the photo paper is what matters. Everything else is just a tool to help you get there.

I am sure any camera you own right now has the capability to produce brilliant images if you are equally capable enough behind the lens. Develop and keep improving your own skills and your images will be amazing. That is the only way to do it. The only way there ever was.

Keep shooting amazing.

*This is now a teeny tiny blog trying to compete with the big guys. If you liked what you read, please take a second to share it. It would help me a lot. Thank you.*

Since you like formulas so much (said no one ever) I haven’t even picked up a camera yet, but my wife is a professional photographer, and demands would like me to learn, so that she doesn’t have to stress over finding reliable double-shooters. So I started this evening with a simple book to grasp the fundamentals, and it wasn’t long before I stumbled upon the topic of exposure – I immediately went in search of an equation to help me understand the relationships between variables – because I love mathematics. For the past hour, I’ve bounced from page to page, and you’ve done an… Read more »