What scope is, and why the ratio matters
Scope is the length of rode you have out divided by the vertical distance from your bow roller down to the seabed. It is the single number that decides whether your anchor digs in or drags, because it controls the angle at which the rode pulls on the anchor's shank.
Every anchor design in common use — plough, scoop, fluke, claw — is engineered to bury itself when pulled roughly horizontally along the bottom. Pull it upward at a steep angle and the fluke rotates out of the seabed instead of deeper into it. At 7:1 scope with the rode straight, the angle at the anchor is about 8 degrees above horizontal; at 3:1 it is nearer 19 degrees; at 2:1 it is 30 degrees, and almost nothing will stay buried. The rode is not what holds the boat — the seabed does — but the rode is what determines whether the anchor can use it.
Two effects work in your favour. First, chain has weight, and its catenary sag flattens the pull further at the shank, which is why all-chain rode can hold well at 5:1 where a rope rode wants 7:1. Second, in a hard blow the catenary straightens and the rode acts as a spring, absorbing surge that would otherwise snatch the anchor out. Both effects disappear as the wind rises and the chain comes bar-taut, which is precisely when you want the extra scope you can no longer veer.
The other half of anchoring arithmetic is the swing circle. The boat pivots about the anchor as the wind or tide shifts, and she lies her full length downwind of the point where the rode meets the water. Your circle has a radius equal to the horizontal reach of the rode plus your length overall, and every point on it must clear other boats, shoals and moorings.
Getting the vertical distance right
The formula is trivial — rode equals scope times height — and every mistake happens in the height.
Start with the depth you actually have. That is what the sounder reads, and it is worth knowing what your sounder is referenced to. Many transducers are set to read depth below the transducer; some are offset to read depth below the keel or below the waterline. A three-foot offset in 15 feet of water is a 20% error in scope.
Add the tide still to come. This is the term most often forgotten, and it is the one that turns a comfortable 7:1 into a marginal 4:1 at three in the morning. Anchor in 12 ft two hours after low water in a place with a 10 ft range and you may be in 20 ft by high water. The scope you set is the scope at the deepest moment, not the shallowest — so use the depth at the next high water.
Add the bow roller height. The rode leaves the boat at the roller, not at the waterline, so the vertical leg of the triangle runs from the roller to the seabed. On a 35 ft sailboat this is typically 3 to 5 ft; on a trawler or a modern flybridge cruiser it can be 6 to 8 ft. Ignore it and you overstate your scope, and by the largest proportion in shallow water: in 10 ft of water with a 5 ft bow, the correct vertical is 15 ft, so 70 ft of rode gives 4.7:1, not the 7:1 you might have assumed.
The swing circle uses Pythagoras. The rode, the vertical distance and the horizontal ground it covers form a right triangle, so the horizontal reach is √(R² − h²). At normal scopes the rode is so much longer than the depth that the horizontal reach is very nearly the full rode length — at 7:1 it is 98.97% of it. Add your length overall and you have the radius. Double it for the diameter, which is the number to compare with the space between you and the next boat.
Worked example: 20 ft of water, 4 ft of tide to come
You are anchoring a 35 ft boat with a bow roller 4 ft above the water. The sounder reads 20 ft, and the tide tables say another 4 ft to come before high water. You want 7:1.
- Vertical distance. 20 + 4 + 4 = 28 ft from roller to seabed at high water.
- Rode to veer. 7 × 28 = 196 ft. Mark your chain at 25 ft intervals and this is eight marks, so veer to just past the 200 ft mark rather than trying to be precise.
- Horizontal reach. √(196² − 28²) = √(38,416 − 784) = √37,632 = 193.99 ft. Notice how close that is to the full 196 ft: the vertical leg barely matters at this scope.
- Swing radius. 193.99 + 35 = 228.99 ft, call it 229 ft, or 76 yards.
- Swing diameter. 458 ft, about 153 yards. That is the circle of water you need entirely to yourself if the wind boxes the compass overnight.
- Check what you carry. With 250 ft of rode aboard, 196 ft leaves 54 ft in the locker — comfortable. The most scope this berth could ever give you is 250 ÷ 28 = 8.9:1.
Now suppose you only carry 140 ft. The most you can achieve is 140 ÷ 28 = exactly 5.0:1, with a horizontal reach of √(19,600 − 784) = 137.17 ft and a swing radius of 172 ft. That is a workable berth in settled weather with all-chain rode, and a poor one if it comes on to blow. The decision the number forces is a real one: move to shallower water, where the same 140 ft buys a larger ratio, or accept the scope and set an anchor watch.
One more case, to show how much the tide term matters. Anchor in 12 ft with a bow roller at the waterline and veer 60 ft: that looks like 5:1. If 8 ft of tide is still to come, the vertical at high water is 20 ft and your actual scope is 60 ÷ 20 = 3.0:1. The rode did not change; the water underneath it did.
How to read the result
Choose the ratio from the conditions and the rode, not from habit. The widely used working figures are 5:1 for all-chain in settled weather, 7:1 for a mixed rope-and-chain rode or for anything less than settled, and 10:1 or more when heavy weather is forecast. In a crowded anchorage where 7:1 would swing you into a neighbour, the honest choice is often to anchor somewhere else rather than to shorten up.
Compare the swing diameter to the space you have. Boats on chain and boats on rope swing differently, and boats of different windage swing at different times, so a neighbour 100 ft away at slack water can be a lot closer when the tide turns. If your swing circle overlaps someone else's, the boat that anchored second is the one expected to move.
Watch the achievable scope figure. It is the reality check: it tells you the best your locker can do at this depth regardless of what you would like. Anything under 3:1 should be read as a warning that the berth is too deep for your ground tackle.
Depth limits are real. With 300 ft of rode and a 5 ft bow, the deepest water in which you can still make 5:1 at high water is about (300 ÷ 5) − 5 = 55 ft. That is why cruising boats carry far more rode than they usually use, and why deep anchorages in the Mediterranean and the Pacific Northwest routinely see boats at scopes that would be considered marginal elsewhere.
Remember what the calculation assumes. It treats the rode as a straight line from roller to anchor. With chain, the real rode sags into a catenary, so the horizontal distance to the anchor is a little less than computed and the angle at the shank is flatter than the straight-line geometry suggests. Both errors are in the conservative direction for holding and in the optimistic direction for swing radius, so treat the swing circle as a slight underestimate.
Rode required by depth and scope
| Vertical, roller to seabed (ft) | 3:1 | 4:1 | 5:1 | 7:1 | 10:1 |
|---|---|---|---|---|---|
| 10 | 30 | 40 | 50 | 70 | 100 |
| 15 | 45 | 60 | 75 | 105 | 150 |
| 20 | 60 | 80 | 100 | 140 | 200 |
| 25 | 75 | 100 | 125 | 175 | 250 |
| 28 | 84 | 112 | 140 | 196 | 280 |
| 35 | 105 | 140 | 175 | 245 | 350 |
| 45 | 135 | 180 | 225 | 315 | 450 |
| 60 | 180 | 240 | 300 | 420 | 600 |
The vertical height is depth at high water plus bow roller height, not the sounder reading alone. Approximate rode angle at the anchor with a straight rode: 19° at 3:1, 14° at 4:1, 11.5° at 5:1, 8.2° at 7:1 and 5.7° at 10:1.
Mistakes that turn a good anchorage into a bad night
- Measuring scope from the waterline. The rode leaves the boat at the bow roller. Omitting 4 ft of freeboard in 16 ft of water turns a genuine 7:1 into 5.6:1.
- Forgetting the tide still to rise. Scope must be set for high water. In a 10 ft range this term alone can halve your effective ratio while you sleep.
- Counting the rode you think you veered. Mark the chain at fixed intervals with paint or cable ties and count the marks. Windlass counters drift, and gypsy slip means the number on the display is not the number over the bow.
- Ignoring the swing circle of the boat that anchored first. The later arrival takes responsibility for clearance. A boat on rope and a boat on chain do not swing in step, and neither does a boat with a lot of windage forward.
- Setting the anchor with a short pull and never checking it. Veer the full scope, back down at increasing power, and take transits ashore or set a GPS anchor alarm sized to the swing radius you calculated, not to an arbitrary 100 ft.
- Assuming holding is the same everywhere. Anchors hold well in sand and firm mud, poorly in soft ooze and weed, and unpredictably in shingle and rock. Scope cannot compensate for a seabed the anchor cannot penetrate.
Beyond scope: what else determines whether you hold
Scope is necessary and not sufficient. Anchor size and type set the maximum holding load; the seabed sets whether that load is achievable at all; and the rode's elasticity determines how much shock loading reaches the anchor when the boat snubs in a chop. On a rope rode, nylon's stretch does that job. On an all-chain rode, the catenary does it until the chain lifts clear, at which point a snubber — a length of nylon taken to a cleat with the chain slack behind it — is what stands between the anchor and repeated shock loads. Most experienced cruisers regard a snubber as compulsory on all-chain rather than optional.
A useful discipline when you arrive is to compute the swing circle before you drop, then drive the circle: motor the radius you are about to occupy and see what is inside it at low water. Charted depths are referenced to a datum — chart datum, typically approximately the lowest astronomical tide — so a 6 ft charted patch at the edge of your circle may be 6 ft at its shallowest, not on average.
Anchoring sits inside the wider planning arithmetic of a passage. The distance you can cover before the light goes depends on your speed, which for a displacement hull is bounded by the hull speed and for a planing boat by the power available through Crouch's formula. Identifying the headland or light that marks the entrance to the anchorage, and knowing at what range it will lift above the horizon, is the job of the distance to horizon calculator. And the waypoint for the anchorage itself usually needs converting between the coordinate formats a pilot book and a plotter use, which the GPS coordinate converter handles.
One last practical point about units. Rode is commonly marked in fathoms on older boats and in metres on European chain; six feet to the fathom, 3.281 feet to the metre. This calculator accepts all three so you can enter the depth in whatever your sounder shows and the rode in whatever your chain is marked in.