Is it really annoying when non car-owners do this?
Non-car owners never grasp:

Petrol cost
Insurance cost
Actual car cost
Parking cost
Road Tax cost
Mot/Servicing.

How do you ask for petrol money without looking petty?

I think you need to formulate your request better! It does not make sense as is.

If they are going were your going you should not ask them,but if you got to to them elsewhere you can ask/

BIB. That's probably because they don't know, because they have no reason to know this information. It's like asking me what is the cost of rice/pound. I have no idea, because I don't buy or eat it. You have to come to some arrangement regarding their contribution towards petrol costs or just stop giving them lifts.

I'm not one to ask or expect a contribution for a 'lift' if it's in my general direction and I have offered the lift. However, anyone who once in the car that delivers the, "oh, i need to go via..." or, "you don't mind if I stop off at xxx first..." or similar etc ... will not ever be offered a lift again. Don't accept a striaghtforward lift and then take advanatge of the offer (or try to) once in the car.

It's your choice to drive and have a car and therefore you should bare the costs associated with it.

If people take the P tho (i know a few who do), then that's really anoying, it's not a charity service, it doesn't run on fresh air.

Have to say, at work the other day, one of the people I work with actually asked to borrow £1 to pay for his raffle ticket!

Personally I think if you offer someone a lift as you are going the same way then you should not ask or expect any money. If you arrange a day out or trip then if it is suggested one person drive then costs should be shared and the person being asked can easily say "that's fine as long as we split the petrol" or if you are the person to offer you could say "look if we all split the petrol we can take my car"

I once gave a colleague a lift to and from work for a week as he couldn't drive due to an injury. It meant going a few miles out of my way, waiting outside his house until he got ready (which was always late) and having to hang around the office until he wanted to go home. It probably added about an hour each day to my commute.

At the end of the weeks he have me an envelope "for your trouble". I wasn't expecting a lot but I was shocked to open it and only find a FIVER inside!

If it's just a one-off then I'll happily do it for nothing as a favour but if you expect me to be your personal taxi driver for a week then it's worth more than a quid a day.

In similar situations, where an amount is agreed (eg £10) the cash doesn't always turn up.....they just "don't have it" or will "get it next week".

In another situation, I was bringing someone back from work and there was a warning sign about a road closure ahead. I said we might have to take a detour....he said "don't want to go too far out of my way" - well this person doesn't drive and hasn't got the first clue about where the alternative local routes are. I could have pulled over and waved the keys saying "here u go then, do a better job" but I couldn't be bothered.

If we're just going somewhere local then I wouldn't dream of asking for petrol money.
We go away for a few weekends a year though and I neath always drive and we split petrol costs then as it's usually a couple of hours away

Depends if they use the car or not.

I wouldnt think to ask for money towards diesel. Though I have a friend who totally takes the piss and I have stopped giving her lifts. I used to take her shopping with me, taking me out of my way about ten miles each time, once or twice a week. She started telling me what time we would be going and on what day etc. But I pay for my car so that I can do things at my convenience, not at hers. She never offered diesel money but that didn't really bug me.

It generally doesn't bother me locally (less than a mile or so), if I'm already out and about.

I did have my partners cousin asking me to make 2 trips a day to the hospital 8 mile away, for a week. 32 sodding miles a day. I drive a big diesel too that drinks fuel for fun unless you're on the motorway.
She said she'd sort out petrol money. Never happened.

i take some satisfaction driving passed her every morning, whilst we are both going to roughly the same place. Especially when it's raining.

Whether it's non-car owners or non car-owners you're talking about, it's hardly worth the bother asking. As you said in the OP, there are various costs with owning a car, so why expect to be paid for the petrol? Provided that you aren't going out of your way for them the extra fuel cost of carrying a passenger is negligible, and any payment would be pure courtesy. You can't really ask someone to be courteous, they either are or they aren't. You just have to quietly judge them.

You have not told us the circumstances in which you're expecting a contribution towards petrol money and why have you listed 5 additional costs associated with car ownership? I know it costs a lot to run a car but you can't expect your passengers to contribute towards your insurance, road tax, etc.

If you're regularly going out of your way to give them a lift then drop some hints about the extra it's costing you in fuel.

Unless it's a case of me saying I'll drive the next time I always at least offer money, although I have a few people who get offended if you offer

The main issue I have is the issue of being bound to be a certain place to pick them up. I will meet u at such and such a place to pick you up......and they don't turn up.

Or, if as the car driver you feel ill and don't want the hassle to doing what was planned because u promised to help somone out.....kinda nullifies the convenience aspect of owning a car.

My old housemate used to take the mick when it came to lifts. He would also make fun of the car, until one day I turned around and pointed out the bus stop over the road and said he could meet me at the place later.

I've also worked with people who would come over asking for a lift (which would take me miles out of the way) and not even offer anything. And be even cheekier and suggest I should pick them up everyday! Making my journey an extra 4 miles each way (8 miles x 4 days is another 32 miles per week) Essentially meaning an extra day driving to where we worked.

Most people do seem quite straight forward though and make the offer in advance and I always do too. I used to go a lift to a woman who paid £15 per week for fuel as it cost £30 each week and that was fair. It would have cost her over £300 per week in a taxi and the busses didn't run at that hour.

Sometimes when I go to see my mum, my brother, (who still lives with my mum) will insist on giving me a lift home even though he isn't going anywhere else in the direction of where I live and refuses every single time to take a penny of payment for it when I offer payment in return.

None of the costs mentioned in the OP are really relevant except petrol and unless it's massively out of the way or an inconvenience because of time or location I wouldn't even bother asking for that. One offs or the occasional lift aren't really that much bother if they're nearby.

Arrangements that become regular like to and from work I'd probably ask for a token amount, maybe £5 a week. Not just to cover petrol but like others have said you're basically commuting yourself to someone else's timing rather than having to worry about yourself.

I've been driving over 10 years but prior to that I've had arrangements with work colleagues where I was paying them petrol money for regular lifts in to work. I didn't mind at the time because it was cheaper and more convenient than getting a bus or taxi. Since I've been driving myself though I now realise what I was paying them in petrol was actually the full cost, maybe a bit more than the full petrol cost. It's no wonder they were quite happy with the arrangement as I was subsidising their travel in to work. Saying that though it was still cheaper and convenient for me so I guess a win/win for both of us.

It started to become a pain though when the work colleague I was getting a lift in with started to regularly have 1-2 days a week where they'd turn up late resulting in us both getting in to work 5-10 minutes late. It wasn't a major thing for her as she worked on the other side of the building and her manager was a pushover. My manager wasn't though and I started getting warnings. He knew that I was getting lifts in and so was dependant on her but of course said it wasn't his problem. When she started giving me lifts she lived in the next estate so it was on her way to stop at my house. A couple of months in she'd moved a couple of miles further away and although she still had to drive straight past my estate she didn't want to go to the bother of driving in to get me and back out to the main road despite it being probably an extra 2 minutes drive. So I then had to walk to the main road for 10 minutes from my house and wait at a bus stop where she'd pick me up at an agreed time every morning.
Despite now being not as convenient for me she insisted on the full petrol money. There were still times I'd turn up at the bus stop and she'd be 10 minutes late so I'd be waiting longer and then get in late.

Then one day I walked up to the bus stop. I was running a little late but made up time by running and got there about a minute later than the agreed time. She wasn't there so I assumed she was running late again anyway so waited.
10 minutes went by and she hadn't turned up so I tried to ring. No answer but I thought she's probably driving so hung up. Another 5 minutes and I rung again. She answered the phone and I asked if she was running late. She said "No, I'm at work. I got to the bus stop and you weren't there and I was going to be late so I thought you were sick!". To say I was pissed off would be an understatement. I ended up having to walk back home then call a taxi after calling my boss and explaining what happened. Also had to make up the time as overtime which meant I couldn't leave the same time as her so had to also pay more to get home.

If she'd turned up on time as she'd claimed then she clearly didn't wait all that long as I was there within a minute. The road was raised away from the footpath and I had to go through an underpass to get to the other side and then up a short slope to the bus stop. I suspect i was just on the other side of the road when she decided to just go. She had my mobile and could have quite easily called to find out what was going on but didn't bother. If she'd done so I'd have been able to say where I was and I'd have been there within a minute.

The one good thing is that was pretty much the final straw and the catalyst for me to get my driving licence. A month later I took an intensive course and passed my test.

you start the conversation with "if we all chip in for petrol".

Petrol, sure, but why is insurance the passenger's problem?

I think I have broached the 'issue' with "If we car share it works out at x pounds per week"

I've always been upfront about the costs and in one case when diesel prices dropped quite a bit I did point out several times that they were paying me too much, and the new figure was significantly lower. They were still happy as it saved them the expense of taxis.

That particular person I also saw out socially so I always made sure to buy them an extra drink or two to make up the difference. Yes, they were essentially buying their own drinks with their own money. But it was the only way I could give it back that they would accept.

I've also car shared with another person and we didn't contributed towards fuel costs as I drove one week and him the other. Sometimes it worked out that it would be one of our turns to drive but we wanted to drink the night before (we were driving at 5 am so drinking the night before wasn't advisable) so we just swapped days around. Perhaps I'd drive 7 days instead of 5 but he could drink and a few weeks later he may drive 6 days instead of 5. It all worked out in the end.

If you offered the lift as a one-off and you were already going in that direction the as a passenger I would be a bit put out if you turned around and asked for a contribution. However, if it's something regular such as car sharing for a journey to work then that's a different thing. The other person is gaining a benefit in either saved time or costs or both, so asking them to chip in a bit wouldn't be an unreasonable request.

Simply ask them how they feel about chipping in. If their argument is that you're going that way anyway then you can suggest that if the favour you're doing them means so little then they won't mind much if tomorrow they find their own way to work.