Ask whether birth time matters and you will get two confident answers. One says the chart is worthless without it. The other says it barely moves anything. Both are describing a different part of the chart and neither says which.
The part that moves
The ascendant is the degree of the zodiac climbing over the eastern horizon at the moment of birth. The Earth turns once in about twenty four hours, which works out at roughly one degree every four minutes. A fifteen minute error moves it about four degrees. An hour moves it fifteen. Four hours will usually carry it into a different sign entirely.
The midheaven moves with it, and because houses are built from the angles, every house placement inherits the same error. That is the whole of what a wrong birth time costs, and it is a great deal.
The part that does not
Sign positions are a separate question. The Sun moves about a degree a day, so it is unaffected by anything short of a calendar error. Mercury, Venus and Mars move at similar rates. Jupiter and the outer planets move so slowly that a whole day would not shift them.
The Moon is the exception, at roughly thirteen degrees a day. That is still only about half a degree an hour, so it only becomes a problem if you were born close to a lunar sign boundary. Whether you were is a fact about your chart, not a general rule, and the test above answers it for you.
Why the answer has to be specific to you
A body sitting in the middle of a house will stay in that house across a four hour error. A body sitting one degree from a cusp can change house on a fifteen minute one. The same is true of the ascendant: born at twenty nine degrees of a sign, a few minutes matters enormously; born at fifteen degrees, an hour is survivable.
General advice cannot tell you which case you are in. Casting the chart seven times and comparing can, and that is all this page does. Nothing is estimated and nothing is smoothed.
What to do with a rounded or uncertain time
Times recorded to the nearest quarter hour are extremely common and usually fine. Times recorded to the nearest hour are worth treating with more caution, and the table will show you whether that caution is warranted in your case or not.
What matters more than precision is honesty about it. A chart built on a guessed time and presented as settled is the real problem, not the guess itself. If your time is approximate, the sign positions are still exactly right and the houses are provisional, and saying so costs nothing.
On rectification
Working backwards from life events to estimate an unknown birth time is a real practice with a long history. This site does not offer it. The reason is the same reason it does not offer personality quizzes that announce your rising sign: the result depends on assumptions that cannot be checked, and a number arrived at that way looks identical to one read off a certificate while being a very different kind of thing.
Common questions
How accurate does my birth time need to be?
For the ascendant, within about four minutes per degree, so a fifteen minute error moves it roughly four degrees. For sign positions of the planets, an hour either way almost never matters. The test shows both on your own chart rather than in the abstract.
What if my birth certificate rounds to the nearest quarter hour?
That is very common and it is usually survivable. A fifteen minute uncertainty leaves the ascendant sign correct unless you were born within a few minutes of a boundary, which the table will show you.
Why does the ascendant move so fast?
Because the Earth turns once a day, so the whole zodiac passes the eastern horizon in twenty four hours. That works out at roughly one degree every four minutes, though the rate is uneven and depends on your latitude.
Can the Moon change sign with a wrong time?
Yes, if you were born near a lunar sign boundary. The Moon covers about thirteen degrees a day, so a few hours can carry it across. The test tells you whether that applies to you specifically.
What is chart rectification?
Working backwards from known life events to estimate an unknown birth time. It is a real practice and a contested one, and this site does not offer it, because the result depends on assumptions that cannot be checked.
Should I bother with a chart if my time is a guess?
For sign positions, yes, they will be right. For houses and the ascendant, treat the result as provisional and say so to anyone reading it. A chart built on a guessed time that is presented as certain is the actual problem.