It is not clear if Sherlock Holmes is rich, but he will need a decent after-tax income to live his lifestyle in modern London (2016): £7680 per month living on his own, or £5460 living with Watson.
Before £12828 per month to live on his own, or £8346 per month with Watson. We'll assume that he doesn't have any student loans or special tax exemptions., he will need to make a rather hefty
Holmes does not seem to have many hobbies apart from his work and stimulating his intellect, and he does not seem to have any external financial commitments either. Hence it is relatively straightforward to estimate his expenses as follows:
- Rent: Two bedroom apartments in Baker Street go for around £3300 per month.
- Housekeeping: It's unclear what Mrs Hudson charges for cleaning and minor catering duties, but housekeepers cost around £7-£10 per hour. Let's say that she does 10 hours of work per week, i.e. 40 hours per month, for £400 per month.
- Taxis: Holmes does not seem to use public transport very much. It's unclear how much he uses taxis, but let's say it is an average of twice per day - more when he is on a case, less between cases. This is 60 times per month, at any time of day or night. If we assume a moderate distance of a few miles for each trip at of £25 per trip, this works out to £1500 per month.
- Clothing: We will assume that Holmes is like Batman or Steve Jobs: he has just enough copies of the same or similar outfit to do his job. : £1350 for his coat, £150-460 for his shirts, £495 upwards for his suits, £500 for his shoes and £308 for his dressing gown. A fully-stocked basic wardrobe might have two coats, ten shirts, four suits, four pairs of shoes and one dressing gown - a total of around £10000. Let's say £12k including socks, underwear and other accessories. He will need to replace his entire wardrobe every five years, thus spending £2400 per year on clothing - i.e. £200 per month.
- Food: Holmes has highly developed senses and tastes, and must therefore require high-quality food. Even if he never eats at restaurants, he will need at least £1000 per month to feed himself high-quality food and wine at home.
Total cost of the above when living on his own: £6400 per month. When he is sharing the rent and housekeeping costs with Watson, this comes down to £4550 per month. Adding 20% for incidentals, this comes to around £7680 living on his own or £5460 living with Watson.
Regarding incidental costs, Holmes is a known cocaine user. It is not clear how much he consumes, but given thatappear to be around £54 per gram (around two taxi trips), I'm going to assume that this falls into his 20% incidentals. His other known habit of violin playing is not expensive in terms of running costs.
The median person living in London earns aroundWhichever way you look at it, Sherlock Holmes needs to be making a lot of money to be a private detective.
Edit: Thanks tofor helpfully pointing out the cocaine and violin habits.