Etymology

cp. OIcel skaði (masc.) ‘harm, damage’ < PGmc *skaþōn; cp. OE sceaða ‘injurious person’ (and rarely ‘injury’, but note sceaðe (fem.) ‘injury’), OFris skatha, OS scatho, OHG scado and further Go skaþis (neut.) ‘harm, injustice’

PGmc Ancestor

*skaþōn

Proposed ON Etymon (OIcel representative)

skaði ‘harm, damage’ 
(ONP skaði (sb.))

Other Scandinavian Reflexes

Far skaði, Icel skaði, Norw skade, ODan skathi, Dan skade, OSw skaþi, Sw skada

OE Cognate

sceaða ‘injurious person’ (and rarely ‘injury’)

Phonological and morphological markers

absence of palatalization of */sk/

Summary category

A1*c

Attestation

Attested fairly widely throughout ME and MnE dial, but especially N and E and alliterative texts (and MED surname evidence (sense 5) comes only from Lan., Lin. and Yks).

Occurrences in the Gersum Corpus

Gaw 674, 2353; Cl 21, 151, 196 etc.; WA 3915

Bibliography

MED scāth(e (n.) , OED scathe (n.) , HTOED , EDD scathe (sb. and v.) Dance scaþe, Bj. 123, de Vries skaði (1), Mag. skaði (1), Bj-L. skade, Orel *skaþōn, Kroonen *skaþjan-, AEW sceaða