schätzen
to estimate
To give an approximate statement about a size, value, or amount without measuring it exactly.
Ich schätze, die Reparatur wird etwa 200 Euro kosten.
I estimate the repair will cost about 200 euros.

to estimate / appreciate
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to estimate
To give an approximate statement about a size, value, or amount without measuring it exactly.
Ich schätze, die Reparatur wird etwa 200 Euro kosten.
I estimate the repair will cost about 200 euros.

The verb 'schätzen' (to estimate/appreciate) is related to the noun 'der Schatz' (treasure). It describes the act of determining or recognizing the value of something.
Ein Experte schätzte den Wert des Gemäldes.
An expert estimated the value of the painting.
When estimating a value or amount, the preposition 'auf' followed by the accusative is often used to indicate the result of the estimate.
Der Polizist schätzte die Geschwindigkeit des Autos auf 100 km/h.
The police officer estimated the car's speed at 100 km/h.
In the meaning 'wertschätzen' (to appreciate/value), 'schätzen' usually refers to people or to abstract things like 'Hilfe' (help), 'Ehrlichkeit' (honesty), 'Freundschaft' (friendship), or 'Meinung' (opinion).
Ich schätze es sehr, dass du immer für mich da bist.
I really appreciate that you are always there for me.
In the meaning 'vermuten' (to assume) or 'glauben' (to believe), 'schätzen' is typically followed by a subordinate clause, often with the conjunction 'dass' (that).
Ich schätze, dass der Zug Verspätung hat.
I guess that the train is delayed.
to know
'wissen' and 'schätzen' can both refer to an assessment in your mind, but they are not the same. Use 'wissen' when you are sure of a piece of information. Use 'schätzen' when you are only judging or guessing a number, amount, or situation approximately. In addition, 'schätzen' can mean that you appreciate someone or something. There is a particular risk of confusion with uncertain information: if you are sure, say 'wissen'. If you are only calculating roughly or guessing, say 'schätzen'.

Im Bus schätzt er, dass die Fahrt mit den Kindern noch eine Stunde dauert.
On the bus, he estimates that the ride with the children will take another hour.
Nina weiß vor der Reise genau, wann der Bus abfährt.
Before the trip, Nina knows exactly when the bus leaves.