Pythagorist
Trigonometry

Bearing Calculator

Convert between compass directions and three-figure bearings instantly. Covers all 16 compass points with step-by-step explanations — ideal for GCSE maths navigation questions.

Result

045°

How it works

  1. Look up compass bearing

    NE corresponds to a bearing of 45°.

    Result:45°

  2. Write as three-figure bearing

    Bearings are always written as three digits: 045°.

    Result:045°

Three-Figure Bearings

Bearing=angle measured clockwise from North (000° to 359°)\text{Bearing} = \text{angle measured clockwise from North (000° to 359°)}
NN000° (or 360°)
EE090°
SS180°
WW270°

Example substitution

NE=045°,SW=225°\text{NE} = 045°, \quad \text{SW} = 225°

NE is 045° and SW is 225° as three-figure bearings.

Worked examples

Write the bearing for North-East (NE).

  1. 1
    Identify compass direction: NE is halfway between N (0°) and E (90°)
  2. 2
    Calculate bearing: NE = 45°
  3. 3
    Write as three-figure bearing: Pad with leading zero: 045°
Answer: Bearing = 045°

A bearing of 225° corresponds to which compass direction?

  1. 1
    Normalise bearing: 225° is already in range 0–360°
  2. 2
    Compare to compass points: SW = 225°
  3. 3
    Identify direction: 225° = South-West (SW)
Answer: Compass direction = SW

Frequently asked questions

What is a bearing?+

A bearing is a three-figure angle measured clockwise from North. E.g., East is 090°, South is 180°, West is 270°.

Why are bearings always three figures?+

To avoid ambiguity — 090° not 90°, 045° not 45°. Always written with three digits.

How do you find the back bearing?+

Add 180° to the bearing (if result ≥ 360°, subtract 360°). E.g., back bearing of 070° is 250°.

What is North as a bearing?+

000° or 360°.

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