MATH 4DAT / Quick reference kit
The number you need.And why it works. 38 fast tools in 5 groups: units, logs & db, ham radio, navigation, algebra & matrices. Every answer shows the formula, the shortcut worth memorising, and the chapter of the book that teaches it.
Units 10 Logs & dB 5 Ham radio 12 Navigation 7 Algebra & matrices 4
Find a tool Units
01 Length Convert length between 9 common units.
01 Mass Convert mass between 6 common units.
02 Volume Convert volume between 10 common units.
02 Area Convert area between 9 common units.
01 Temperature Convert °C, °F, and kelvin. Temperature needs an offset, not just a factor.
03 Angle Convert angle between 6 common units.
18 Speed Convert speed between 5 common units.
20 Pressure Convert pressure between 7 common units.
18 Energy Convert energy between 8 common units.
18 Power Convert power between 6 common units.
Logs & dB
10 Logarithm Find log₁₀, ln, log₂, or a log in any base.
10 Antilog and powers Undo a logarithm: raise a base to a power.
10 dB → ratio and % Turn a gain or loss in decibels into a power ratio, voltage ratio, and percent.
10 Ratio or % → dB Compare an output to an input and get the change in decibels.
10 dBm ⇄ watts Move between dBm, dBW, watts, and milliwatts.
Ham radio
05 Frequency ⇄ wavelength Find wavelength in free space and inside coax.
21 Dipole and vertical length Cut lengths for a half-wave dipole, quarter-wave vertical, and 5/8-wave whip.
10 SWR from the meter Translate an SWR reading into reflected power, return loss, and real loss.
10 SWR from forward and reflected power Use a wattmeter's forward and reflected readings to find SWR.
19 Impedance and match Turn R + jX into magnitude, phase, and SWR on your line.
10 ERP and EIRP Add antenna gain, subtract feedline loss, and find radiated power.
10 Coax loss How much power reaches the antenna through a length of cable.
21 LC resonance Find the resonant frequency of a coil and capacitor.
21 Reactance Reactance of a coil and a capacitor at one frequency.
10 S-meter to dBm Convert an S-unit reading to signal power and voltage.
10 Free-space path loss Estimate line-of-sight loss for VHF, UHF, and microwave links.
06 Ohm's law and power Voltage and current give resistance and power.
Navigation
07 Sextant altitude corrections Turn a raw sextant or phone reading (Hs) into the true observed altitude (Ho).
11 Latitude from the noon sun Measure the sun at its highest point and find your latitude.
11 Latitude from Polaris In the northern hemisphere, the height of the North Star is almost your latitude.
03 Longitude from the time of noon Time the sun's highest point by a UTC clock and find your longitude.
11 Sight reduction (line of position) Compare your sight with the altitude you should see from an assumed position.
11 Distance and bearing between two positions Shortest distance and starting course between two latitude/longitude points.
19 Phone tilt → altitude (digital sextant) How a phone turns its gravity sensor into a sextant angle, and how accurate that can be.
Algebra & matrices
08 Quadratic equation Solve ax² + bx + c = 0, including complex roots.
08 Linear equations (3 unknowns) Solve three equations in x, y, z at once.
20 Eigenvalues (2×2) Find the stretch factors and special directions of a 2×2 matrix.
20 Eigenvalues (3×3) Solve the characteristic cubic of a 3×3 matrix.
Units · Book chapter 01: Measurement, Units, and Precision
Length Convert length between 9 common units.
Converted 3.048 m
1 ft equals 0.3048 m
1 m equals 3.28084 ft
Model to = from × (from factor ÷ to factor)
Every length conversion is one multiplication. The inch is defined as exactly 25.4 mm, so feet, yards, and miles convert exactly too.
Shortcuts to remember 1 in = 25.4 mm (exact) 1 ft = 0.3048 m (exact) 1 m ≈ 3.281 ft ≈ 39.37 in 1 mi = 1.609 km; 1 km ≈ 0.621 mi 1 nautical mile = 1,852 m = 1 minute of latitude Read how Castle’s 1899 Chapter 1 teaches the idea → FIELD USE NOTICE These tools are educational planning aids. Radio figures are typical values; check your equipment’s datasheet and your licence rules. Phone and hand-held sextant fixes are a backup and a teaching aid — never the only means of navigation.