Two pulls, one anchor
A snatch block anchor is not carrying the line pull. It is carrying the vector sum of two rope tensions that both pull away from the block, and the size of that sum is set by the angle between them. When the two parts of the rope are parallel and pointing the same way — the rope doubled straight back on itself — the sum is the two tensions added. When they point in opposite directions, meaning the rope is running straight through, they cancel.
The formula for equal tensions is two times the tension times the cosine of half the angle between the parts. At zero degrees between the parts that is 2.000 times. At 45 degrees, 1.848. At 90 degrees, 1.414. At 120 degrees, 1.000 — the anchor sees exactly the line pull and no more. At 180 degrees, nothing.
The defaults, worked through
A 4,000 lb line pull at 96 percent sheave efficiency means 4,000 lb in one part and 3,840 lb in the other. With 45 degrees between them, the resultant is 7,243 lb, which is 1.81 times the line pull. It points 22 degrees off the incoming part and 23 degrees off the outgoing one — near enough the bisector, and not exactly it, because the two tensions are not equal.
Turn the same rope right back on itself and the number goes to 7,840 lb. Let it run nearly straight and it collapses toward zero. The winch never knew the difference.
Efficiency shifts the direction, not just the size
The sheave takes a few percent out of the rope as it goes round, so the outgoing tension is slightly lower than the incoming one. That has a small effect on the size of the resultant and a visible one on its direction: the bisector tips toward the higher tension. It is a small thing, and it is the reason the page prints both angles rather than assuming a clean bisector.
Redirecting is not the same as doubling
Two different jobs get done with the same block. A block hung on the load and pulled through gives mechanical advantage — twice the force at the load, half the speed. A block tied to an anchor to send the rope round a corner gives none. People mix these up constantly, and the anchor load arithmetic on this page is the same either way, because the anchor only ever sees the two rope tensions and the angle between them.
The strap around the tree is a second problem
Everything above stops at the block. Whatever attaches the block to the anchor has its own geometry, and if that is a strap with two legs, those legs multiply the resultant again by their own angle in exactly the way a sling does. It is the same trigonometry as a lifting bridle, and it is worth doing rather than assuming the strap is the easy part.
Questions people ask
How much force does a snatch block put on its anchor?
Between zero and twice the line pull, set entirely by the angle between the two parts of the rope. For equal tensions it is two times the tension times the cosine of half that angle. Doubled straight back on itself gives 2.000 times; 90 degrees between the parts gives 1.414; 120 degrees gives exactly the line pull; running straight through gives nothing.
Is the anchor load the same as the winch line pull?
At one angle only, around 120 degrees between the two parts of the rope. Below that the anchor sees more than the line pull, up to twice it. Above it the anchor sees less. Assuming the anchor sees the line pull is safe on one side of that angle and badly wrong on the other, which is why the angle is the input rather than an afterthought.
What is the deflection angle versus the included angle?
They add up to 180. The included angle is measured between the two parts of the rope as they leave the block, so zero means the rope doubles back. The deflection angle is how far the rope has been bent off straight, so zero means it is not being turned at all. Charts use both and the page takes either.
Which way does the force on the anchor point?
Along the line that splits the two rope parts. With a frictionless sheave that is the exact bisector; with real sheave efficiency the two rope tensions differ slightly and the resultant tips toward the higher one. The page prints the angle off each part, because an anchor that is strong one way and weak another cares about the direction more than the size.
Does adding a snatch block double my pulling power?
Only if the block is on the load and moving with it. A block fixed to an anchor to change the rope direction gives no mechanical advantage at all. Both arrangements load the anchor the same way, by the vector sum of the two rope tensions, so the anchor arithmetic on this page does not care which job the block is doing.
Does this tell me whether my anchor will hold?
No. It gives you the force and its direction, and it stops there. What the anchor is, how it is made, what the soil or the wall or the tree is doing, and whether the strap and shackle between block and anchor are up to it are all questions for someone looking at the actual setup, with the manufacturer ratings for the actual hardware in hand.