Calculating pH from [H₃O⁺] and vice versa

pH is a measure of the [H₃O⁺] in a solution.  Because [H₃O⁺] are usually very small, it is convenient to use a logarithmic scale to describe hydronium ion concentration, and pH is defined as shown below.
 

pH = - log10 [H3O+] where [H3O+] equals the concentration of H3O+ in mol L–1

Consider pure water
[H₃O⁺] = 0.0000001 = 1 × 10^–7
pH = –log [H₃O⁺] = 7
Show Calculator
 The examples below show how to use your calculator to deduce pH from given [H₃O⁺] and vice versa.
 

pH = - log10 [H3O+]	Doing this on calculator	displays this
Example 1: Calculate the pH of a solution where  [H3O+] is 6.02 × 10-4 mol L–1. Answer: pH = - log10(6.02 × 10–4)  pH = – (–3.22) = 3.22	Enter digits before ×  then E (or EXP)	6.02e
	then the exponent	6.02e-4
	then log	-3.22
	then change sign (+/-)	3.22

 

[H3O+] = 10–pH	Doing this on calculator	displays this
Example 2:  Calculate [H3O+] for a solution where  pH 4.76.   Answer:  -log10[H3O+] = 4.76  log10[H3O+] = -4.76  [H3O+] = 10–4.76 [H3O+] =1.74 ×10–5	numbers then +/-	–4.76
	SHFT(2nd) then log or 10^	10^( )
	Enter or =	1.7378–05
	Write the result as	1.74×10–5