Ascendant
The date places the Sun and the Moon.
The rising sign moves about one sign every two hours. A missing time is not guessed.
The city sets the time zone. The clock of the computer you are using does not.
The Earth turns. The sign on the eastern horizon changes about every two hours, a little faster or slower depending on the sign and the latitude. That is why two people born on the same day, in the same city, can have different rising signs. The date fixes the Sun. The time and the city fix the horizon.
If the time is missing, there is no rising sign. Averaging the day, or using noon, produces a chart that looks finished and is wrong for half the people born that day. This page leaves the rising blank instead.
A time within about ten minutes is usually enough, unless you were born near the moment the rising sign changed. If you only know the hour, cast it and then cast it an hour later. If the rising sign stays, you can read the houses. If it changes, you do not have a rising sign yet. A birth certificate is better than a relative's memory of the afternoon.
People meet the rising sign first and the Sun later, once they know you. A Libra rising with an Aries Sun can look agreeable and then decide fast. The horoscope for the Sun still applies to the Sun. It does not describe the rising sign. The pair of them is on the sun-and-rising pages. The full set of houses is the birth chart.
Free Synastry Chart Calculator
1°43′ Ta · Singapore
Orbit · the month
The sign is free. The house, the aspects, and the written line stay open with Orbit.