## The Math of Exposure Values

Exposure Values are a somewhat important concept, kind of, if you are trying to maintain consistent exposure while fiddling with your camera in manual mode.  Realistically, by shooting in aperture or shutter priority, with your ISO locked down, your camera will maintain the proper exposure value for you anyway.

A photographer might need to prepare for any values between -6 and 16, and the difference of 1 exposure value is called a “stop”. Remember, though “stopping down” generally refers to using a narrower aperture, you can also decrease your shutter speed or ISO by one stop!

The actual math of this does not matter too much to a normal photographer. Or an abnormal photographer. It’s somewhat fascinating to think about this if you are designing experiments or writing software that does crazy camera things though.

Honestly, if you’re doing crazy math-based camera experiments, you probably didn’t need to read this. However, I’m upset that the equations for the exposure triangle (which dictate the relationship between iso/shutter speed/f-number) are not readily available without you solving for these elements yourself, so I figured I’d commit them to one place on the internet. If you need these, look no further.

Note many resources will give versions of these equations using EV_100, or Exposure Value at ISO100. No standards body has codified use of EV_100, and while some websites claim that “Light Value” refers to non-ISO100 EV (and sometimes the opposite, EV_100), this is inconsistent with contradicting definitions around the internet. Forget about light value, for now it’s not a useful term, it’s the math photography equivalent of “nonplussed”. Just use these equations, and if you want ISO100 or EV_100 plug in 100 for the ISO.

If these all feel like they are yielding answers that are just a littttle off-  welp, congratulations, you’ve learned the dirty secret of photography.  The fnumbers are very, very slightly rounded.  Below is mathematically sound, where:

• F is the relative aperture (f-number)
• t is the exposure time (“shutter speed”) in seconds
• S is the ISO arithmetic speed
• EV is the exposure value

## ISO

S = \frac{100 \times F^2}{t \times 2^{EV}}
Python
iso = (100 * (fnumber ** 2))/(shutter_speed * (2 ** exposure_value))

## APERTURE

F = \sqrt{ \frac{S \times t \times 2^{EV}}{100} }
Python
import math
fnumber = math.sqrt(((iso*shutter_speed) * (2 ** exposure_value))/100)

## SHUTTER SPEED

t = \frac{100 \times F^{2}}{S \times 2^{EV}}
Python
shutter_speed = (100 * (fnumber ** 2))/(iso * (2 ** exposure_value))

## EXPOSURE VALUE

EV = \log_2(\frac{100 \times F^2}{S \times t})
Python
import math
exposure_value = math.log2((100 * (fnumber ** 2))/(iso * shutter_speed))

There!

If these are useful for even one photography nerd blossoming into an engineer nerd, then this was completely worth it!