USCG Exam Prep
Formula & Quick-Reference Sheets
The working formulas you'll reach for on the chart-navigation, deck, and rules modules — compass error, set & drift, time-speed-distance, stability, light arcs, and the give-way cheats.
🧭 Compass Error (TVMDC)
- The order
- True · Variation · Magnetic · Deviation · Compass — “True Virgins Make Dull Companions.”
- Compass → True
- ADD easterly errors going up the page: True = Compass + Deviation + Variation (East +, West −).
- True → Compass
- SUBTRACT easterly errors going down: Compass = True − Variation − Deviation.
- Rule of thumb
- “East is least (subtract), West is best (add)” — when converting True → Compass.
- Compass error
- Compass error = Variation + Deviation (algebraic sum, watching E/W signs).
🌊 Set, Drift & Current
- Set
- The DIRECTION the current flows TOWARD (true). Found as the bearing from your DR to your fix.
- Drift
- The current's SPEED in knots = distance (DR→fix) ÷ time elapsed.
- Course made good (CMG)
- The actual track over the ground — DR course corrected for the current.
- Course to steer
- Lay off the current vector, then swing your boat speed to the desired track; the boat heading is the course to steer.
- SOG
- Speed over the ground — the length of the resultant (ground) vector per unit time.
⏱️ Time · Speed · Distance
- Distance
- D = S × T (distance in nm, speed in knots, time in hours).
- Speed
- S = D ÷ T.
- Time
- T = D ÷ S.
- “60 D Street”
- 60 × D = S × T (with time in minutes). Cover the unknown: D = S×T/60, S = 60D/T, T = 60D/S.
- 3-minute rule
- In 3 minutes a vessel travels (speed in knots) × 100 yards. 12 kn → 1200 yds in 3 min.
⚖️ Stability
- Metacentric height
- GM = KM − KG. Positive GM = stable; zero = neutral; negative = unstable (lolls).
- Righting arm
- GZ ≈ GM × sin(heel) for small angles. The horizontal distance between the buoyancy and gravity lines.
- Free surface effect
- Liquid in a slack tank acts as a virtual rise of G — it REDUCES GM. Press tanks up or empty them.
- Stiff vs tender
- Large GM → stiff, short snappy roll. Small GM → tender, slow easy roll.
- Listing moment
- Moment = weight × distance off centerline (ft-tons). Off-center weight lists the vessel.
- Raising/lowering G
- Weight added high raises KG (less stable); added low lowers KG (more stable).
🔦 Light Arcs
- Masthead light
- 225° — right ahead to 22.5° abaft the beam on each side.
- Sidelight
- 112.5° each — right ahead to 22.5° abaft the beam on its side.
- Sternlight
- 135° — 67.5° each side of right astern.
- All-round light
- 360°.
- Towing light (yellow)
- 135°, above the sternlight.
- Combinations
- 2 sidelights + sternlight = 360°. Masthead + sternlight = 360°.
📢 Give-Way & Sound Signals
- Pecking order
- NUC/RAM → Constrained by Draft → Fishing → Sailing → Power-driven (each keeps clear of those above).
- Crossing
- Vessel with the other on her STARBOARD side gives way; the other stands on.
- Head-on
- Both alter to STARBOARD, pass port-to-port.
- 1 / 2 / 3 short blasts
- Altering to starboard / altering to port / operating astern propulsion.
- 5 short blasts
- Danger or doubt signal.
- Fog (power-driven)
- Making way: 1 prolonged ≤2 min. Underway but stopped: 2 prolonged ≤2 min.
Put it into practice
Drill these on the interactive chart plotter and 2,300+ exam questions. Free to start.