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What's the difference between at hand, on hand and in hand? At hand seems to me as if you have something in reach. On hand is if you have something in stock. And in hand can be used as if you have more time at your disposal.

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Did you look in a dictionary? – slim Jan 17 '12 at 14:12

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The way these different prepositions are used is all very much idiomatic, so there will be a limit to how far you can "rationalise" why any particular preposition is associated with any particular meaning. Especially in respect of "hand", since most of us always have a couple of those about our person ready to be incorporated into our word choices.

One thing I would say that "in" usually denotes something closer than "on" (which itself is usually closer than "at"), which is why the "nearby" meanings use the latter two.

Note that "in hand" doesn't actually mean having more time at your disposal - it's just that we often say we have "time in hand" (things in hand can be in reserve, spare). Apart from the literal held in the hand, the other common idiomatic usage for this one is that if something is "in hand" it's being actively dealt with (by implication, really close to you), not just sitting on your "to-do" list.

OP doesn't mention to hand, which is actually more common than the others in British English (but seemingly quite rare for Americans). In practice few would choose at hand or on hand on the basis of how physically close/accessible something was - largely pointless anyway, since few others would apprehend any subtle distinction being made. Go British and make life easier for everyone!

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"In hand" is also, I think, the only one of the three that's used literally (as in, pen in hand, ...). – onomatomaniak Jan 17 '12 at 15:05
@onomatomaniak: I guess that depends how you define "literally" in the case of "at", but I certainly think you're right about "on". I can't think of any "literal" usage for that one. "He's got LOVE and HATE tatoos on hand"? Hmm - I don't think so! – FumbleFingers Jan 17 '12 at 15:12
...just for the hell of it - Q. "Have they engraved my writing set yet?" A. "They did the pencil and ballpoint yesterday, and they have the pen in hand today". – FumbleFingers Jan 17 '12 at 15:17
In means contained, and that refers to one's physical hand, which is for containing things, among other uses. So all the uses of in hand are metaphorical extensions of a grasping hand with something (like a tool, for instance) in it. – John Lawler Jan 17 '12 at 16:50
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@FumbleFingers: Thanks, I will go with to hand. I don't have my card to hand right now, but I can look it up for you. Right? – user17857 Jan 19 '12 at 4:00
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At hand frequently refers to proximity in time, the other two usually relate to spatial proximity:

With the apocalypse at hand, I was pleased to find I have a cache of food and water on hand, and a rifle in hand.

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I'd never seen (at least, never noticed) "at hand" used for that "imminent" sense before, but checking Google Books for war at hand shows you're quite right. Primarily American usage, I guess. +1 for that, and for managing to get all three prepositions in one sentence. I read the last one as rifle in reserve, spare, rather than actually being held, but I suppose it's just ambiguous. – FumbleFingers Jan 19 '12 at 4:30
American English uses 'at hand' in that sense a lot. "The time is at hand" is another common instance. – Lynn Jan 19 '12 at 5:21
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Think of measures of distance:

in hand - literally within one's grasp - not even inches away - "A bird in the hand"

at hand - nearby - a few feet away at most - "He kept his cigarettes at hand"

on hand - somewhere accessible but fairly distant - more than a few feet away and less than a few hundred yards - "We have more vacuum cleaners on hand"

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