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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

Nick Summers assesses how other key turnaround leaders are faring, from Nokia’s Stephen Elop to United’s Jeffrey Smisek.
The CEO Hail Mary: A Scorecard on Corporate Change Agents Nick Summers February 28, 2011

Former Homeland Security chief Michael Chertoff assesses the danger—and how we can battle the enemy within.
Our Homegrown Terror Threat Michael Chertoff December 31, 2009

Expert Canada-watcher Chris Sands assesses yesterday’s election in Alberta as a big win for … President Obama.
Obama Wins in Alberta David Frum April 23, 2012

Jace Lacob assesses the field to see whether Mad Men will make history with a fifth win.
Emmys Drama Race: ‘Mad Men,’ ‘Downton Abbey,’ ‘Breaking Bad,’ and More Jace Lacob September 17, 2012

It’s a “news segment” from Fox & Friends that assesses Obama’s first four years in office.
Shocking, Even for Fox Michael Tomasky May 29, 2012

Historical Examples

For this service Xanabar assesses her percentage, therefore Xanabar is rich.
History Repeats George Oliver Smith

But it is a demand for this surplus, no matter how created, that assesses the value of the whole product.
The Rural Magazine, and Literary Evening Fire-Side Various

Ef he’s got somewhars ’round ten dollars in chicken-feed an’ in ones an’ twos, you assesses him dues of jest one dollar even.
J. Poindexter, Colored Irvin Shrewsbury Cobb

He condemns a whole street at a time, assesses the damages, pays them, and rebuilds superbly.
The Innocents Abroad Mark Twain (Samuel Clemens)

The more severe government of France assesses upon each generality a certain sum, which the intendant must find as he can.
An Inquiry into the Nature and Causes of the Wealth of Nations Adam Smith

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.