Blue hour is the handful of minutes when the Sun is just below the horizon and the sky turns a deep, even blue. City lights are already on. The sky is still brighter than the buildings, so a single exposure can hold both. That balance is the whole point.
On this site, blue hour is the time the Sun sits between 4° and 8° below the horizon. That is the usual photographer definition (the same band timeanddate.com uses). It is around civil twilight (Sun 0° to −6°), but it is not the full civil-twilight window — the first minutes after sunset are often still warm. The first minutes after sunset are often still warm, so the calculator also shows sunrise and sunset for the walk-in.
Evening (night) blue hour
This is the one most people mean. After sunset the warm colour drains, the sky goes cobalt, and streetlights, windows and signs start to match the sky. In Budapest that window is often 20–40 minutes, longer in June, shorter in December. If you arrive at sunset you still have time to pick a corner and wait. If you arrive when the sky is already indigo, you are late for the balanced frame and early for a night shot with a black sky.
Morning blue hour
Same physics, opposite order. The sky lifts from black to blue before sunrise, then the colour warms. Morning is quieter: fewer people on the bridge, shop signs off, river traffic down. You have to be in place in the dark. The calculator’s morning start is your latest sensible arrival, not the time to leave the apartment.
What it is not
It is not “an hour.” Near the equator it can be 15 minutes. At 47°N in June it can stretch past 40. It is also not a filter. If the sky is grey from low cloud, you get a grey hour. The colour needs a clear or high-cloud sky so the remaining sunlight can scatter.
Use the calculator for the times. Use your eyes for the last two minutes — when the sky and the lights sit at the same brightness, take the frame.