Angle Converters
Last updated: 2 June 2026
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Guide
Angles: From Carpentry to Satellite Dishes
You're installing a satellite dish and the instructions say "set the elevation to 31.5 degrees". You're fitting a skirtings board in a modern home with an unusual ceiling angle. You're a carpenter working with a mitre saw and need to cut at exactly 35 degrees. These all require understanding angles, but in different contexts with different precision levels.
Degrees are the everyday unit. A full circle is 360 degrees. A right angle is 90 degrees. A straight line is 180 degrees. This is how you learned it in school and how most people think about angles. When someone says "that wall leans about 10 degrees", you probably visualise that reasonably well. Degrees break into 60 minutes (not time minutes, angle minutes), and each minute breaks into 60 seconds. This is why precise navigation uses notation like 151 degrees, 34 minutes, 12 seconds. You probably don't use this unless you're surveying or navigating.
Radians are the mathematician's unit. One radian is the angle swept by an arc equal to the circle's radius. A full circle is 2π radians, or about 6.283 radians. Most people never use radians in real life, but if you're programming, doing physics, or working with trigonometry, radians are essential. Your calculator has a degree/radian toggle. Use degrees for practical work. Use radians for maths.
Carpentry and building rely on degrees constantly. A standard roof pitch in Australia is often 25-30 degrees. Roof trusses are cut to angle based on degrees. A mitre saw calibrated in degrees lets you cut corners at precise angles. For example, cutting a 90-degree corner might require a 45-degree cut on each piece. If you're framing walls or cutting skirting boards, mistakes compound quickly, so getting the angle exact matters.
Navigation uses degrees differently. A compass bearing of 175 degrees means almost due south (180 degrees is exactly south). Pilots, sailors, and hikers use degrees from 0-360, where 0 is north, 90 is east, 180 is south, and 270 is west. GPS coordinates use degrees, minutes, and seconds. You might navigate to 37 degrees, 48 minutes, 23 seconds south, 144 degrees, 57 minutes, 30 seconds east (a location in Victoria). Phone GPS shows decimal degrees (37.8065 south, 144.9583 east), which are easier for computers but less intuitive for humans.
Satellite dishes use elevation and azimuth angles. Elevation is the angle up from the horizon (0 degrees is on the horizon, 90 degrees is straight up). Azimuth is the compass direction. For an NBN satellite dish in Sydney, you might need 31 degrees elevation pointing northwest at 315 degrees azimuth. Getting these wrong means no signal. Most installers use a smartphone app that overlays angles on your view, which is much easier than using a protractor.
Astronomy uses angles for star positions, and photography uses angles for field of view. A camera lens might be 35mm (equivalent), which gives a field of view of roughly 63 degrees. An 85mm lens is narrower, about 29 degrees. Wide-angle lenses (24mm) capture 84 degrees. This matters if you're doing landscapes (wide) versus portraits (narrow). Binoculars and telescopes similarly specify field of view in degrees.
Common Questions
What's the difference between degrees and radians?
Degrees are everyday: 360 degrees = full circle, 90 degrees = right angle. Radians are for maths: 2π radians = full circle, π/2 radians = right angle. Your calculator has both modes. Use degrees for practical work and construction. Use radians if you're coding trigonometry or doing calculus.
What angle should a roof be pitched in Australia?
Depends on climate and aesthetics. Most Australian homes have 20-30 degrees pitch. Cooler, wetter areas might use steeper (30-40 degrees) for water runoff. Hotter areas might use gentler. Check your council building guidelines. A roof pitch of 25 degrees is typical for a suburban Melbourne home.
How do I use a mitre saw to cut a 45-degree corner?
Set the saw to 45 degrees. For an outside corner, cut both pieces at 45 degrees facing opposite directions. This creates a 90-degree corner when joined. For an inside corner, cut at 45 degrees and fit them different way. Mark your pieces clearly so you don't cut them backwards.
Why do compass bearings go 0-360 instead of 0-180?
Because a full circle is 360 degrees. 0 is north, 90 is east, 180 is south, 270 is west. Using the full 360 degrees lets you specify any direction precisely. A bearing of 137 degrees means southeast, roughly. This works for navigation, surveying, and astronomy.
What's the difference between elevation and azimuth for a satellite dish?
Azimuth is the compass direction you point (0-360 degrees). Elevation is how high above the horizon you point (0-90 degrees). A satellite at 31.5 degrees elevation and 315 degrees azimuth is north-northwest, fairly high up. Wrong either angle and you won't get signal.
How do I convert between degrees, minutes, and seconds?
There are 60 angle-minutes per degree, and 60 angle-seconds per minute. 37 degrees, 48 minutes, 23 seconds = 37 + (48/60) + (23/3600) = 37.8064 decimal degrees. Most GPS apps use decimal degrees now, but surveying still uses the minutes/seconds format.
How We Verify Our Conversions
Every converter on RefDat uses peer-reviewed conversion factors sourced from the International Bureau of Weights and Measures (BIPM), the National Institute of Standards and Technology (NIST), and the Australian National Measurement Institute (NMI). Temperature formulas follow the ITS-90 international temperature scale. Cooking measurements use Standards Australia definitions (AS 1766) where applicable. We cross-check against multiple authoritative sources and test every calculator both forwards and backwards before publishing. If you spot an error, let us know.