Explosives in Quake are a little complicated. Not, surprisingly enough, in the way that they can push you about: any old damage can give you a push, and explosive damage works just the same way as all the other types there. However, the way in which the amount of damage done (and hence also the size of the push you get) is calculated can be a little counter-intuitive.
The first thing to say is that rockets are the only explosives that can do direct hit damage. If a rocket hits its target, it imparts full damage to it. It also causes splash damage to everything in the vicinity apart from the thing it hit. All other explosives only do splash damage; hitting the target directly just causes them to explode next to the target and ensures it is near the middle of the splash. Exactly how splash damage works is explained later.
The second weird thing is that your own rockets and grenades only do half the damage to you that they do to everybody else. Who can say why? This means that although player explosives are about three times as powerful as most monster ones (a rocket or grenade can do up to 120 damage, whereas an ogre-grenade or vore-ball does only 40) they aren't so much more damaging as far as the player who fired them is concerned. You can rocket-jump a lot higher if an enemy player fires the rocket below you as you jump - try it out!
Splash damage works from a central point at which the explosion occurs. The further you are away from the centre, the less damage you will take. Beyond the distance where you would take damage equal to half the original splash damage from the explosion minus nineteen points, the splash damage ceases entirely. So you can't do only one or two points damage by catching something at the very extremes of the logical damage radius; the least damage you can do is a bit less than half the splash total.
Of course, the distance measured is between the origin of the
explosion and the origin of the the entity being hurt. The origin of
an entity is normally at its centre. Since there will be a bit of a
gap between an explosion on the floor and the centre of your body when
you rocket-jump, the most damage you are likely to do yourself jumping
straight up is around 53 - a bit less than the full 60. In turn, 60 is
the regular maximum 120 splash damage a player rocket does, halved
because it is your own rocket. The minimum is 21 - rounded, that's
half of 41, which is 19 less than 60, which is half the regular
maximum. Got all
that?