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to estimate officially the value of (property, income, etc.) as a basis for taxation.
to fix or determine the amount of (damages, a tax, a fine, etc.):
The hurricane damage was assessed at six million dollars.
to impose a tax or other charge on.
to estimate or judge the value, character, etc., of; evaluate:
to assess one’s efforts.
Contemporary Examples

There are several problems involved in assessing the value of such tests.
Passenger Flights Must Stop Carrying Lithium-Ion Batteries as Cargo Clive Irving May 4, 2014

Yet unfortunately, Americans are not, however, nearly so accurate at assessing national trends.
Less Fear, Fewer Guns David Frum July 22, 2012

Sitting on my couch, assessing my apartment, Jim said, “I like that print.”
My Friend James Foley: ‘I Just Love Being Where the Story’s Happening’ Sheila Sharma May 15, 2011

assessing rape allegations gets still more challenging in the Middle East, where even the suspicion of rape can break families.
Escaping Assad’s Rape Prisons: A Survivor Tells Her Story Jamie Dettmer October 27, 2014

My trip takes the reverse path, and I begin by assessing the depth of my Shakespeare knowledge in his birthplace.
Biking With the Bard Kara Cutruzzula December 27, 2014

Historical Examples

The250 plots of these four owners are evidently brought together into a virgate for the purpose of assessing the services.
Villainage in England Paul Vinogradoff

He was good at assessing physical values, and he felt scared.
Colorado Jim George Goodchild

They did not object to the tax itself, but to the king’s assessing it by his own authority.
Charles I Jacob Abbott

Others have forbidden the practice of political committees of assessing office holders for campaign purposes.
Government in the United States James Wilford Garner

Marion said that, no doubt, after a hard day at assessing, such a sight would be soothing to a man.
Our Elizabeth Florence A. Kilpatrick

verb (transitive)
to judge the worth, importance, etc, of; evaluate
(foll by at) to estimate the value of (income, property, etc) for taxation purposes: the estate was assessed at three thousand pounds
to determine the amount of (a fine, tax, damages, etc)
to impose a tax, fine, etc, on (a person or property)
v.

early 15c., “to fix the amount (of a tax, fine, etc.),” from Anglo-French assesser, from Medieval Latin assessare “fix a tax upon,” originally frequentative of Latin assessus “a sitting by,” past participle of assidere “to sit beside” (and thus to assist in the office of a judge), from ad- “to” (see ad-) + sedere “to sit” (see sedentary). One of the judge’s assistant’s jobs was to fix the amount of a fine or tax. Meaning “to estimate the value of property for the purpose of taxing it” is from 1809; transferred sense of “to judge the value of a person, idea, etc.” is from 1934. Related: Assessed; assessing.