3:1 scope in 100 ft of water with 10 ft of tide

Rode to pay out

404ft

3:1 over 112 ft of rise — 100 ft depth + 10 ft tide + 2 ft bow height

Rode length	404ft
Total rise100 depth + 10 tide + 2 bow — measured from the bow roller, not the waterline	112ft
Swing radiusthe circle you need clear of other boats and shoal	387ft
Swing diameterif the wind boxes the compass	775ft
Nominal scope	3:1
Effective scoperope floats and pulls up on the anchor — needs more	3.6:1
Rode type	all rope
At the 7:1 overnight standardmore than you are paying out now	941ft

Charted depth: 100 ft
Tidal range: 10 ft
Bow height: 2 ft
Scope: 3
Rode: all rope

Measure the rise, not the depth

Scope is rode length divided by the rise — and the rise is not the charted depth. It is depth plus tide plus the height of your bow roller above the water:

100 ft + 10 ft + 2 ft = 112 ft

At 3:1 with all rope, that is 404 ft of rode.

The bow height is the part people leave out. The anchor holds because of the angle the rode makes at the seabed, and that angle starts where the rode leaves the boat, not where it enters the water.

Tide, before you set

A tidal range of 10 ft means scope calculated at low water shrinks as the tide floods. Anchors drag on a rising tide, in the dark, when the boat you carefully anchored clear of is suddenly much closer than it was.

The number nobody calculates: swing radius

387 ft. That is the circle you need clear of other boats, moorings and shoal water — 775 ft across if the wind boxes the compass overnight.

More scope holds better and swings wider. In a crowded anchorage that trade-off, not holding power, is usually what limits you.

Set it, then check it

Back down at low revs until the boat stops moving with the rode taut. Take a transit on shore and watch it for a few minutes. An anchor that has not been set is a heavy object lying on the bottom, and it will tell you so at three in the morning.

Notes

Measure the rise from the bow roller, not the waterline. The anchor is held by the ANGLE of the rode at the seabed, and that angle starts where the rode leaves the boat. On a boat with 2 ft of bow height in 100 ft of water, leaving it out overstates your scope by 2%.
Add the tide before you set, not after. 10 ft of range means a 3:1 scope at low water becomes 3.6:1 at high — anchors drag on the flood, in the dark, when the boat you anchored clear of is suddenly close.
3:1 is a fair-weather, someone-on-watch scope. Overnight practice is 7:1, which here would be 941 ft of rode. Short scope is the most common reason anchors drag.
Rope pulls upward on the anchor shank as it tensions, which is why it needs more scope than chain. A chain leader of at least a boat length keeps the pull at the anchor horizontal and takes the chafe on the bottom.
Set it properly once it is down. Back down at low revs until the boat stops moving with the rode taut, then take a transit on shore and watch it for a few minutes. An anchor that has not been set is just a heavy object lying on the bottom.

Nearby sizes

"Anchor Weight per Foot: The Rule of Thumb, and Where It Breaks"A pound per foot is a rule that works in the middle of its range and fails at both ends, for two different reasons.
Fluke Anchors: Where They Excel, and the Two Bottoms That Defeat ThemThe fluke anchor has the best holding-to-weight ratio in common use and two well-known failure modes. Both are about the bottom, not the size.
Reading a Modern Scoop Anchor Chart, and What Its Small Print AssumesModern anchor charts look interchangeable and are not. The difference between them is usually one line of small print about assumed wind speed.
Anchoring a 24-Foot Boat: The Questions the Chart Cannot SeeTwo 24-foot boats can need different anchors. Length is the index every chart uses and the one variable that tells you least about the load.