Yes

you do need a jacket based on the weather in Eskilstuna, Sweden 1 second ago

Why? Because it's pretty chilly.
53°F11°C & Partly Cloudy

Wind is 6 mph9 km/h from the SW, gusting to 15 mph24 km/h
September 24
4pm53°F11°C6 mph10 km/h SWPartly Cloudy
5pm52°F11°C6 mph10 km/h SWPartly Cloudy
6pm51°F11°C6 mph10 km/h SWPartly Cloudy
7pm51°F10°C7 mph11 km/h SWMostly Cloudy
8pm51°F11°C7 mph12 km/h SWCloudy
9pm51°F11°C8 mph12 km/h SWMostly Cloudy
10pm51°F11°C8 mph12 km/h SWCloudy
11pm52°F11°C8 mph12 km/h SWCloudy
September 25
12am52°F11°C8 mph13 km/h SCloudy
1am52°F11°C9 mph14 km/h SCloudy
2am52°F11°C9 mph15 km/h SCloudy
3am54°F12°C10 mph15 km/h SCloudy
DateLowHighWindDayNight
September 2351°F10°C61°F16°C11 mph17 km/h from WMostly ClearMostly Cloudy
September 2451°F10°C63°F17°C10 mph17 km/h from SCloudyMostly Cloudy
September 2553°F12°C67°F19°C6 mph10 km/h from SWMostly CloudyCloudy
September 2654°F12°C68°F20°C8 mph13 km/h from SMostly CloudyMostly Cloudy
September 2753°F12°C67°F19°C8 mph13 km/h from SMostly CloudyMostly Cloudy
September 2855°F13°C62°F17°C10 mph17 km/h from SWDrizzleMostly Cloudy
September 2951°F11°C61°F16°C10 mph15 km/h from WMostly ClearMostly Clear

Yes

Low of 51°F11°C, High of 64°F18°C
Wind: 10 mph17 km/h
Precipitation: None

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