# 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.

## 1 Answer

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%.

• I don't understand what your doing, but i think you are right. I will see how it works, and accept your answer :) Thanks! – Refilon Feb 4 '15 at 0:03
• @Dennis: What do you have difficulty understanding? I could try to add more explanation if I knew more about what you have problems with. – Henning Makholm Feb 4 '15 at 0:05
• I don't really understand why you are doing the formula's. What's 0.018 for example? How do you get it? Btw, im no math expert like you guys, just wanted this for my webshop xD – Refilon Feb 4 '15 at 8:28
• @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
• 0.982 = 100 - 1,8 = 98.2. 98.2 / 100 = 0.982 So when i muliply by 0.982 I got TOTAL - 1,8% right? – Refilon Feb 4 '15 at 10:43