As with any game, behind the game mechanics are hit point counters. You can think of player health as hit points, and think of shield and object health as durability... but the numbers are on the same scale. 1 hit point of damage removes 1 point of durability or 1 point of health. Thus, the following will simply be described as points.
You can examine the damage values of most attacks through Spar mode. In that mode, players are awarded points exactly matched to the damage they do to the other player. For example, a single blackjack knife primal does 1 point of damage to a player, shield, ember, or other target. Using these base values, you can then calculate the points of any other game mechanic, even those that only occur outside spar mode.
The following numbers and explanations are a best estimate by fans. They may be slightly inaccurate in places. You may wish to retest them in game yourself, which will also help you understand them better.
Primal Attacks
Every class has a primal attack and a hand shield. Primals can be checked directly in spar mode. Hand shields can only be checked by throwing primals against them, and durability values may be imprecise due to variability of aim. Shields were generally measured by throwing blackjack primal knives against their center.
Anarchist fireball, points by size: 3, 4, 8
Blackjack knives, points by count: 1, 2, 3; 9 with overcharge
Kineticist trash, points by size: 5 (small/medium), 13 (heavy)
Drifter primals, min-max: 2-15 (smooth variability as the ball grows)
Electromancer primals (3-24 points) have some complex behaviors and require more explanation.
The hand shows 4 bulbs which light up as it charges. After all four bulbs are lit, there's an additional "overcharge" phase where the bulbs turn yellow. The primals can be released tap-tap-tap-tap one at a time, each taking a bulb; or, the trigger can be held giving a "full hand" primal where the entire charge is released in one continuous shot from overcharge down to nothing left. The full hand does more damage than the total of the tap-tap shots that would occur from the same initial charge; that is, continuous shooting is more damaging than individual separate shots.
Additionally, electromancer's primal can be boosted by the presence of a power station pole generated from an ember shield. This is the only class whose ember ability includes boosting their hand primal.
A regular bulb, single tap, does 3 points of damage, for the 3 normal bulbs, for a total of 9 points of damage by tapping. The fourth bulb which also holds the overcharge does a total of 6 points of damage by tapping, making the hand primal 15 points total by tapping, provided it started fully (over)charged.
A continuous full-hand primal from overcharge through all bulbs does a total of 18 points of damage, equivalent to one additional bulb more than tapping would give.
A continuous full-hand primal with power station boost does a total of 24 points of damage. This is equivalent to 8 bulbs of charge, though as it's delivered, it hits the opponent ten times. A power station booster not only recharges the primal faster, it also delivers more total damage from a full charge; more even than the drifter's largest ball and on-par with some ember attacks.
In addition, the electromancer also has a hand shield which can store charge to be used as an attack, for up to 10 points of additional charge, giving the EM a grand total of 34 points of damage they can do in a single primals attack, provided a power station is present.
Hand Shields
Hand shields have durability in the sense that as they absorb or reflect primals, they will gradually take damage until they break completely. You can turn off the hand shield to give it a chance to heal/recharge. If you do not turn it off, it will not heal until it is completely broken, and then it must heal completely before it's usable again. It's to your advantage to let it heal before it's fully broken.
Center-blocking an attack deals the attack's damage to the shield and then reflects the (unchanged) primal back out, where it maintains its hit points. For example, a single blackjack knife carries 1 point of attack power. It will deal 1 point of damage to a hand shield when center-blocked, and then reflect back towards the caster. If the caster center-blocks, their hand shield takes 1 point of damage, and it reflects again. It can reflect an unlimited number of times, and does not lose charge. When someone's hand shield fully breaks and the knife strikes a player, it will deal 1 point of damage to that player. Likewise, the overcharged triple knife, at 9 points of damage, would deal 9 points on each shield hit, and eventually deal 9 points of damage to a player. The attack values above are the same points regardless of whether it's a shield, player, or other target that is hit.
The points of damage that each class's shield can absorb, center-blocked, before it's fully broken, are as follows (this could use a retest).
Anarchist hand shield: 12 points
Blackjack hand shield: 24 points
Kineticist hand shield: 18 points
Drifter hand shield: 14 points
Electromancer hand shield: 10 points. (This also means an EM hand shield can store 10 points of charge.)