利用者:紅い目の女の子/十進角
Precision
[編集]The radius of the semi-major axis of the Earth at the equator is 6,378,137.0 m resulting in a circumference of 40,075,016.7 m.[1] The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.5 m or approximately 111.32 km. As one moves away from the equator towards a pole, however, one degree of longitude is multiplied by the cosine of the latitude, decreasing the distance, approaching zero at the pole. The number of decimal places required for a particular precision at the equator is:
| decimal places |
decimal degrees |
DMS | Object that can be unambiguously recognized at this scale | N/S or E/W at equator |
E/W at 23N/S |
E/W at 45N/S |
E/W at 67N/S |
|---|---|---|---|---|---|---|---|
| 0 | 1.0 | 1° 00′ 0″ | country or large region | 111.32 km | 102.47 km | 78.71 km | 43.496 km |
| 1 | 0.1 | 0° 06′ 0″ | large city or district | 11.132 km | 10.247 km | 7.871 km | 4.3496 km |
| 2 | 0.01 | 0° 00′ 36″ | town or village | 1.1132 km | 1.0247 km | 787.1 m | 434.96 m |
| 3 | 0.001 | 0° 00′ 3.6″ | neighborhood, street | 111.32 m | 102.47 m | 78.71 m | 43.496 m |
| 4 | 0.0001 | 0° 00′ 0.36″ | individual street, large buildings | 11.132 m | 10.247 m | 7.871 m | 4.3496 m |
| 5 | 0.00001 | 0° 00′ 0.036″ | individual trees, houses | 1.1132 m | 1.0247 m | 787.1 mm | 434.96 mm |
| 6 | 0.000001 | 0° 00′ 0.0036″ | individual humans | 111.32 mm | 102.47 mm | 78.71 mm | 43.496 mm |
| 7 | 0.0000001 | 0° 00′ 0.00036″ | practical limit of commercial surveying | 11.132 mm | 10.247 mm | 7.871 mm | 4.3496 mm |
| 8 | 0.00000001 | 0° 00′ 0.000036″ | specialized surveying (e.g. tectonic plate mapping) | 1.1132 mm | 1.0247 mm | 787.1 μm | 434.96 μm |
A value in decimal degrees to a precision of 4 decimal places is precise to 11.132 m at the equator. A value in decimal degrees to 5 decimal places is precise to 1.1132 m at the equator. Elevation also introduces a small error: at 6,378 m elevation, the radius and surface distance is increased by 0.001 or 0.1%. Because the earth is not flat, the precision of the longitude part of the coordinates increases the further from the equator you get. The precision of the latitude part does not increase so much, more strictly however, a meridian arc length per 1 second depends on the latitude at the point in question. The discrepancy of 1 second meridian arc length between equator and pole is about 0.3 metres because the earth is an oblate spheroid.