Advanced iPhone Calculator


Today’s Question: I was reading your very interesting article on bit depth in Pixology magazine, and wanted to follow along by doing the math involved with bit depth. However, the calculator on my iPhone only provides basic functions without support for exponents. Is there an app you recommend that provides more advanced functions?

Tim’s Quick Answer: You can actually calculate exponents and other advanced math operations by simply rotating your iPhone to horizontal when using the built-in Calculator app.

More Detail: At first glance the default Calculator app included on the iPhone seems to only offer the very basic mathematical operations of addition, subtraction, multiplication, and division. However, that’s only the case when holding the iPhone vertically, in which case you’re only seeing the basic calculator.

If you rotate your iPhone to horizontal (making sure that rotation isn’t locked) the Calculator app will switch to scientific mode. This will provide you with significantly more options for calculations, including exponents and roots, trigonometric functions, and more.

In the article on bit depth in the December 2023 issue of my Pixology magazine, I outlined the math involved with calculating how many tonal and color values would be available at different bit depths.

For example, with 8-bit per channel you can calculate the number of shades of gray available on each channel by raising two to the power of eight. On a scientific calculator that would involve using the “x to the y” button, which shows the letter “x” with the letter “y” in superscript to indicate an exponent. You can press the number 2 (the base in this case), then the “x to the y” button, and then the number 8 (the number to raise to), which will provide you with the result of 2 raised to the power of 8, which is 256.

To calculate the total number of color values available for an 8-bit RGB image, you need to take the value of 256 and raise it to the power of three. This is represented as the “x to the power of 3” button, which shows the letter “x” with the number “3” in superscript. So, you can simply enter “256” and then press the “x to the power of 3” button to get the result of 16,777,216 total possible tonal and color values for an 8-bit per channel RGB image.