Yes

you do need a jacket based on the weather in Reykjavík, Iceland 1 second ago

Why? Because it's pretty chilly!
53°F12°C & Cloudy

Wind is 5 mph8 km/h from the East, gusting to 6 mph10 km/h
September 15
8am55°F13°C5 mph9 km/h EastCloudy
9am56°F13°C6 mph9 km/h EastCloudy
10am56°F13°C5 mph8 km/h EastCloudy
11am56°F14°C5 mph8 km/h NortheastCloudy
12pm56°F13°C4 mph7 km/h EastCloudy
1pm56°F13°C4 mph7 km/h SoutheastCloudy
2pm55°F13°C5 mph8 km/h SoutheastCloudy
3pm54°F12°C4 mph6 km/h SouthCloudy
4pm53°F11°C3 mph4 km/h SouthCloudy
5pm52°F11°C2 mph4 km/h SoutheastCloudy
6pm51°F10°C3 mph5 km/h EastCloudy
7pm50°F10°C4 mph6 km/h EastCloudy
DateLowHighWindDayNight
September 1449°F9°C56°F14°C5 mph8 km/h from EastCloudyDrizzle
September 1546°F8°C54°F12°C4 mph7 km/h from EastDrizzleDrizzle
September 1643°F6°C50°F10°C8 mph13 km/h from NortheastPartly CloudyPartly Cloudy
September 1739°F4°C47°F8°C11 mph17 km/h from NortheastMostly ClearPartly Cloudy
September 1838°F3°C46°F8°C10 mph17 km/h from NortheastMostly ClearClear
September 1935°F2°C45°F7°C8 mph13 km/h from NorthPartly CloudyMostly Cloudy
September 2038°F4°C49°F9°C10 mph16 km/h from SouthMostly CloudyMostly Cloudy

Yes

Low of 46°F8°C, High of 55°F13°C
Wind: 4 mph7 km/h
Precipitation: 47% rain

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