The verb "taper" is defined in dictionaries as:

To become gradually narrower or thinner toward one end.

So, this word is often used with the adverb "down". I am searching for a word that means To become gradually wider or thicker toward one end. Is it possible to use the expression "taper up" for the meaning?

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    Since you wrote "this word is often used with the adverb 'down'", you should add some examples. I am curious if up or down is really needed. – user3169 May 7 '18 at 5:14
  • Counter-example: An obelisk is a stone object that tapers up to a pointed end. – cobaltduck May 7 '18 at 17:00
  • The words comes from an older word for (dipped) candle. up is not the opposite of down in the context of phrasal verbs. – Tᴚoɯɐuo May 7 '18 at 21:26
  • @rama9: You should really present to us a close analogue of the final statement you wish to make with this word, as there is no guarantee that any word offered to you will be idiomatic in the sentence you want to plug it into. For example, we wouldn't say The delta thickens as it nears the ocean but we might well say The wooden plank thickens and it needs to be jointed and planed down. – Tᴚoɯɐuo May 8 '18 at 11:36
  • If my language is literally translated into English, the following sentence is created: The width of the shaft increases from one end in a tapered manner. After consult dictionaries, I felt that this is strange. Then, I has created the following sentence "The width of the shaft tapers up from one end". For some reasons, I want to use the word "one end" not "the other end". – rama9 May 9 '18 at 1:30

If you put an opposite word of an adverb, it does not convert the word into the opposite meaning.

slow down cannot be turned into slow up to mean faster!

The word you may use is flared which means widening up. Though it has limited usage and may not suit to your concern.

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    What's interesting is that both slow up and slow down mean the same thing. – user3395 May 7 '18 at 12:19
  • "Flared out" refers to something having a wide portion, usually at an end. "Flare up" refers to a fire becoming more obvious. (This sense of "flare up" can also be used metaphorically.) – Jasper May 7 '18 at 19:25

You wouldn't get the meaning you're looking for if you said 'taper up'. The immediate thing that comes to mind when I hear 'taper up' is a tall building 'tapering up' toward the sky. In this case the adverb is referring to the direction that the thinner end would point if it tapered to a point. You could also say 'tapered to the right' for instance.

That doesn't mean that 'tapered down' always means that the tapered end points down, though. 'to taper down' is a verb phrase that means the same thing as 'to taper'. The word 'down' in this case is not referring to the direction, but to the width getting smaller or lower.

It would be perfectly acceptable to simply say

"became gradually thicker toward one end"

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A baseball bat broadens out above the handle.

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To taper just means to become thinner as the length increases, or as you move along the length. down is only used as a direction, it's not a phrasal verb. There is a phrasal verb to taper off, but it has a different meaning: to diminish over time, not over space.

Both wider and thicker (in your question) have related verbs:

to widen

to thicken

However, to thicken has connotations of food: to thicken the sauce. To widen looks like the word you want.

The beam widens the further from the source it gets.

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First, it's most usually used with "off", as in "taper off". "Down" would be valid but a distant 2nd. The nearest and most popular antonym to "taper down" would be "spread out", followed by "fan out", "enlarge", or "thicken"

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In what context?

Gradually reducing something (like doses of medication) over time, is often called tapering down, (sometimes, tapering off), so logically we might expect gradually increasing something to be tapering up.

Oddly, I've never heard that.

However, "ramping up" is widely used in the context of gradually increasing something, for example, Tesla is ramping up production of its new car.

For something physical you can simply turn round and look at from the other end, I think "taper" is OK but I agree "taper up" is a little strange, perhaps "widen" or "thicken" at one end is better.

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AS your question already hit on, you're looking for the word "widen."

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