# How to calculate percentage of an amount

I don't know if this is the right forum to ask, but i need to have a % from an amount, and hope there is a formula to calculate it.

Example:

Some payment methods have a 1.8% fee of the total amount a user has in their shopping basket. Now i want, that if the user selects one of those payments, that they have to pay those 1.8%. but when i charge them 1.8% extra i will still have to pay for the payment method (not all, but still a bit)

e.g. a user has shopped for € 100. Now i ask 1.8% more, that's 100 x 1.018 = 101.80. But now i have to pay 1.8% of 101.80 to my "middleman". So i still only get 101.80 * 0.982 = 99.9676. Now that doesn't seem too bad, but i would like to have a percentage that i have to put on the price so i have the right amount left when i payed the fee to my "middleman".

i hope you get what i mean. I need a % = TOTAL_AMOUNT + 1.8% when i have to pay.

If you want to have a net of $N$ left after the middleman takes 1.8% of the gross price, the gross price should be a number $G$ such that $$G\times(1-0.018) = N$$ We can solve this by dividing by $(1-0.018)$ on both sides, and get $$G = \frac{N}{1-0.018}$$
If you want to convert that to a percentage markup, calculate $$\frac{1}{1-0.018} = 1.018330$$ So you should mark your desired prices up by 1.833%.
• @Dennis: $0.018$ is just 1.8% written out in full. Your question shows you already know how to increase something by 1.8% by multiplying by $1+0.018$, and decrease something by 1.8% by multiplying by $1-0.018$, so I assumed that wouldn't confuse you. How do you think about the number $0.982$ that appears in your question, for example? – Henning Makholm Feb 4 '15 at 10:28