⚓ Navigation Calculator

Mercator calculation + Calculator instructions (Casio fx-82EX)

The same A and B positions above are used for every tab. Enter coordinates, pick a mode, then run its calculate button.

Calculator steps use Casio fx-82EX.

Departure (A)

Place search:

Results:

Latitude: ° '

Longitude: ° '

Arrival (B)

Place search:

Results:

Latitude: ° '

Longitude: ° '

Mean latitude and Mercator sailing (MP A/B, DMP) — the usual chart-work base for course and distance.

Mercator formulas (forward & inverse)

I want to find:

Name	Route (A → B)	Actions

Mean latitude between A and B: average of signed latitudes; used for departure at mean latitude.

Mean-latitude formulas (forward & inverse)

Great circle: shortest path. Initial true bearing from A and distance (Earth R ≈ 3440.065 NM).

Great-circle formulas (forward & inverse)

ETA = departure time + (distance ÷ speed). Use last Mercator or GC distance, or type NM manually.

ETD (local):

Departure timezone:

Arrival timezone:

Legs (distance & speed per leg)

“Last Mercator/GC” use the last result from that tab. If one is missing, the other is used automatically (with a note in the answer).

Current set = bearing toward which the current flows. Desired track = ground track. Solver finds course to steer and SMG.

V+S=G — definitions, paper method and example

When current and desired track are given, the goal is the vector triangle with V+S=G. V: through water; S: set (direction current flows) and drift (speed); G: track over ground (COG/SMG). This app uses the same math as a correct paper solution.

Ship speed (kn):

Drift rate (kn):

Set (° toward):

Desired track (°):

Compass rose (true)

Stømkopling (forward): ground track = through-water vector + current vector; set = direction toward which the current flows (same rose).

Reverse: desired track and current given — find course to steer (through-water heading on this rose).

Drills use the A/B positions above (Mercator, mean latitude, great circle) or self-contained scenarios (passage time, set and drift).

Mini screens match fx-82EX: type the top line, press [=]. D = degrees; use R for GC radians. Updated when you open this tab or press New exercise.

Practice: Mercator

New exercise fills A and B. Enter true course and rhumb-line distance from the Mercator formulas, then check.

Calculator display (for current A and B):

Your answer — true course (°):

Your answer — distance (nm):

Practice: mean latitude

Positions stay in one hemisphere. Give mean latitude (decimal °, N + / S −) and departure at mean latitude in nm.

Calculator display (for current A and B):

Mean latitude φm (decimal °):

Departure at φm (nm):

Practice: great circle

New exercise fills A and B. Enter initial true bearing from A and great-circle distance.

Calculator display (for current A and B):

Initial bearing (°):

Distance (nm):

Practice: passage time

Passage time on the calculator:

Your answer — passage time (hours, two decimals):

Practice: set & drift

ClassWiz (D mode): type each line and [=]. Use Ans after steps 1–2 as on the real calculator. Example trial course H° is shown in steps 3–4 — change H until step 5 matches your desired track.

Your answer — course to steer (°):

CASIOfx-82EX ClassWiz

D/R

Tap each step. Top line: what you type on fx-82EX before pressing [=] (D for Mercator/mean-lat; R for great-circle radian steps). Bottom: the answer after [=].