Anchor Angles and Force on Each Piece
A two-piece anchor is a simple vector problem, and the vector math is unforgiving: the wider the V between the legs, the more load each piece carries. At 120 degrees each piece already carries the full climber; at 170 degrees it carries almost six. This guide shows where those numbers come from and where the red lines sit.
The formula
The load hangs from the master point; each anchor leg holds a tension T whose vertical component must carry half of it. If the angle between the legs is θ, the vertical component of each tension is T · cos(θ/2), and the two together must equal the load W:
T = W / (2 · cos(θ/2))
The anchor force calculator evaluates this for any load and angle, and reports the multiplier - how many times the climber's weight each piece feels. The key values:
| V angle | Per leg | Reading |
|---|---|---|
| 0° | 0.50 × W | Perfectly parallel - the ideal you never get |
| 60° | 0.58 × W | Excellent; barely worse than parallel |
| 90° | 0.71 × W | Good - the practical working angle |
| 120° | 1.00 × W | Each piece carries the full load - the ceiling |
| 150° | 1.93 × W | Almost double - outside safe practice |
| 170° | 5.74 × W | Nearly sixfold - an anchor in name only |
Why 120 degrees is the red line
At 120 degrees the multiplier crosses 1.0: each piece feels the whole climber, the master point feels more than the climber, and any dynamics - a factor-influenced catch, an uneven pull, a piece beginning to lift - push real forces beyond the clean formula. The past-120° regime is also the least controllable one, because the multiplier's growth is not linear: 30 degrees of extra width costs 0.3× at 90° but nearly 4× between 150° and 170°. The habit worth building: check the V at the master point, not the rock.
Practical geometry
- Extend toward a common point. Slings on the pieces let you narrow the V at the master point even when the placements are wide; the formula cares about the angle where the load hangs.
- Equalize deliberately. A cordelette tied off static assumes equal arms; if one leg is looser, the taut one takes the lion's share whatever the V says.
- Watch the direction of pull. The formula assumes the load pulls straight down between the pieces; a traverse or a pendulum rotates the real angle, usually for the worse on one leg.
- Three pieces beat two wide ones. A third arm narrows the effective V and adds redundancy - placement quality still decides which pieces actually take the fall.
The other half of the severity story is the catch itself: how hard the rope yanks the anchor in the first place is the fall factor's business, quantified by the fall factor calculator. The two tools answer the two halves of one question - how hard the system is hit, and how the hit is shared.
Frequently asked questions
What assumptions does the per-leg formula make?
Static equalization: both legs are tied off equal, the load hangs from a single master point, and friction in the system is ignored. Under those assumptions each leg carries W / (2cos(theta/2)). Real anchors with unequal leg lengths let the taut leg take most of the load regardless of the V angle - which is why equalizing matters as much as geometry.
Is a 90-degree angle acceptable?
Yes - each leg carries about 0.71 times the load, a comfortable margin. The working rule is to keep the V under 90 degrees when you can and treat 120 degrees as the absolute ceiling, because beyond it every extra degree buys force fast: 150 degrees puts 1.93 times the load on each piece and 170 puts nearly six times.
How does a sliding X change the picture?
It self-equalizes, so the geometry math holds even if the legs are not perfectly equal - but the runner extends if one leg fails, adding a shock load, and the carabiner at the master point sees both strands rubbing. Many teams use a sliding X with a limiter knot for the redundancy benefit and accept the extension trade-off.
The angle is dictated by the placements - what then?
Extend the pieces with slings toward a common direction. A wide stance can be narrowed into a clean V by lengthening the arms that reach toward each other; the force formula cares about the angle at the master point, not where the gear sits in the rock. Placement quality first, then geometry - never the reverse.