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Arc Minutes to Degrees

Arc Minutes to Degrees

Change the minutes part of a chart position, bearing or magnetic variation into the decimal degrees a plotter, routing file or spreadsheet accepts.

Chart Minutes and the Decimal Degrees a Plotter Wants

Navigation is the last trade that still counts angles in minutes as a matter of routine. Latitude and longitude are ruled off a paper chart in minutes, a GPS shows a fix as degrees and decimal minutes, magnetic variation is printed on the compass rose in degrees and minutes, and a hand bearing taken across the water is read to the nearest whole degree. The moment any of that has to be typed into route-planning software, a spreadsheet of waypoints or a passage log, it has to become a single decimal number.

Conversion factor: 1′ = 1/60° = 0.01666667°, so minutes divided by 60 give the decimal part. A waypoint written 51° 27.500′ N becomes 27.5 ÷ 60 = 0.458333, or 51.458333° N — and because a minute of latitude is a nautical mile by definition, those 27.5′ are also 27.5 nautical miles north of the 51st parallel.

Where Minutes Turn Up on Passage

Positions off the chart

Chart borders are graduated in minutes and tenths, so a fix plotted with dividers is naturally read as degrees and minutes rather than as a decimal fraction of a degree.

Variation and deviation

The compass rose gives variation as something like 3° 15′ W with an annual change in minutes, and a deviation card lists residual error the same way before either is applied to a course.

Waypoint entry

Chartplotters and aviation units default to degrees and decimal minutes, but routing tools, mapping libraries and almost every file format expect one signed decimal degree per axis.

Distance run

Because a minute of latitude is a sea mile, the difference in latitude between two fixes read straight off the side scale is a distance as well as an angle — which is exactly why the unit survived.

Working a Fix or a Bearing Through the Fields

Convert the minutes part on its own and add it back to the whole degrees — that keeps the sign and the hemisphere in your hands rather than in a formula.

1

Enter only the minutes

For 51° 27.5′ type 27.5 in the left field, not the whole coordinate. The decimal degree result appears as you type; a comma is accepted as the decimal mark, which helps when the figure was copied from a European almanac.

2

Add the whole degrees back on

Add the result to the degrees part, then apply the hemisphere: north and east stay positive, south and west take a minus sign. Getting that sign wrong is the error that puts a waypoint in the wrong ocean.

3

Reverse it to read a plotter figure onto paper

When the number came from software as 51.458333 and you want it on the chart, press swap (↔) and feed in the fractional part — 0.458333° comes back as 27.5′, ready to step off with the dividers.

4

Copy the plain number into the log

The copy button on either field gives the bare digits with no symbol attached, so a passage log, a customs form or a routing file gets a clean value that will not be rejected by a strict field.

Minutes and seconds are not the same notation. A coordinate written 27.5′ means twenty-seven and a half minutes; one written 27′ 30″ means the same position but in a different format. Feeding 27.30 into a decimal-minutes field instead of 27.5 misplaces the position by about 370 metres — a mistake that is easy to make when transcribing between a printed pilot book and a plotter.

Chart Minutes, Decimal Degrees and Distance Run

Measured along a meridian, a minute of latitude is a nautical mile by definition — 1852 metres exactly since the international agreement of 1929. That makes the middle two columns interchangeable in a way no other pair of angle and distance units manages.

Arc minutes (′) Decimal degrees Along a meridian (nmi) Metric distance
1′ 0.016667° 1 1.852 km
5′ 0.083333° 5 9.26 km
10′ 0.166667° 10 18.52 km
15′ 0.25° 15 27.78 km
30′ 0.5° 30 55.56 km
45′ 0.75° 45 83.34 km
60′ 60 111.12 km

The nautical-mile column holds only for latitude. Run the same minutes along a parallel and the distance shrinks by the cosine of the latitude: 0.866 of a mile at 30°, 0.707 at 45°, and exactly half a mile at 60°.

What Helps at the Chart Table

Both halves of a coordinate in one sitting

Values update on every keystroke, so latitude minutes and longitude minutes can be worked one after another by overtyping the field rather than starting again.

Plotter figure back onto the paper chart

The swap button turns the pair round so a decimal fix from software becomes the minutes you actually step off with dividers along the side scale.

Tenths of a minute stay visible

Results run to eight decimals, so a fix quoted to a tenth of a minute — roughly 185 metres — is not quietly rounded away before it reaches the log.

Values a routing file will accept

Copy hands over digits alone, with no degree sign or hemisphere letter to strip out before the number goes into a waypoint list or a spreadsheet.

Questions from the Chart Table

Why does my GPS show 51° 27.500′ rather than a single decimal number?

That layout is degrees and decimal minutes, the default on marine plotters and most aviation receivers, and it exists so the display matches the chart in front of you. Because the minute is also the sea mile, a navigator can subtract two readings and get a distance without any further arithmetic. Decimal degrees, the third common format, is what software wants; degrees-minutes-seconds is the older survey-style notation. All three describe the same point, and mixing them up in a waypoint list is a classic source of grounding reports.

Is a minute of longitude also a nautical mile?

Only on the equator. Meridians converge towards the poles, so the ground distance covered by one minute of longitude is the cosine of the latitude times a mile: 0.87 miles at 30°, 0.71 at 45°, 0.50 at 60°, and nothing at all at the pole itself. Navigators call the east-west distance departure and compute it from the difference in longitude and the mid-latitude. Latitude is unaffected, which is the whole reason the mile was tied to it.

How far off track does a one-minute steering error put me?

Very little on a coastal leg, and rather more on an ocean crossing. The old one-in-sixty rule says one degree of error over sixty miles run puts you one mile off; a single minute is a sixtieth of that, so after 60 miles you are about 32 metres to one side. Carry the same error for 600 miles and it becomes roughly a third of a mile. What matters more in practice is that a hand bearing compass is rarely better than a degree or two, so minutes of steering error are noise beside the instrument itself.

Should variation be applied in minutes or as a decimal?

Whichever you use, do the arithmetic in one unit. Charts print variation as, say, 6° 15′ W with an annual change of a few minutes east, and rolling those minutes forward for the chart's age is where the fractions matter. Turning 6° 15′ into 6.25° before adding or subtracting it from a true course is usually less error-prone than juggling degrees and minutes separately — and it is the form a plotter or routing program will expect anyway.

Why is distance always measured off the side of the chart, never the top?

The side scale is latitude, and on the Mercator projection a minute of latitude is a mile at every point on the sheet. The top and bottom scales are longitude, where a minute is worth less than a mile everywhere except the equator — stepping dividers along them would overstate the distance. There is a second subtlety: because Mercator stretches towards the poles, the correct practice is to take the mile off the latitude scale at the same height on the chart as the leg being measured, not from the corner.

°

Chart Minutes and Distance

1 ′=0.0166667 °
6 ′=0.1 °
15 ′=0.25 °
30 ′=0.5 °
45 ′=0.75 °
60 ′=1 °

Arc Minute (′)

A sixtieth of a degree, and along a meridian one nautical mile — 1852 m — which is why chart borders and plotters are still graduated in minutes and tenths.

Degree (°)

The whole-number part of a position and the unit a course is steered in. Routing software, mapping libraries and log files all want it as one signed decimal.

Enter only the minutes part, then add the whole degrees and the hemisphere sign yourself
A minute of latitude is one nautical mile, so the same figure doubles as a distance
Press swap (↔) to turn a decimal fix from software back into minutes for the dividers
Positions never leave your device — the arithmetic is done in the browser
Want to learn more? Read documentation →
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