Concert pitch is the actual pitch that an instrument sounds when playing. This is sometimes different from written pitch in that the written pitch of certain instruments, like the trumpet, will sound different from what we hear. To transpose a trumpet to concert pitch, you must know the notes of the chromatic scale and then transpose all of the trumpet pitches down to the correct level. Because the trumpet plays in Bb, you must transpose the notes down to get the correct concert pitch.
Add two flats to the key signature. If the key signature consists of sharps, you will have to remove two sharps. For instance, a key with two sharps will have no sharps or flats after changing the key signature. A key with one sharp will have one flat.
Transpose the note written in the trumpet part down two half steps and one letter name. Use the chromatic scale to transpose notes. The chromatic scale consists of 12 notes that consist of half steps: C | C#/Db | D | D#/Eb | E | F | F#/Gb | G | G#/Ab | A | A#/Bb | B. For instance, if the trumpet has a C written, the transposed pitch would be Bb and not A#. A# is the same pitch as Bb, but it is two letters away instead of one.
Continue to transpose the rest of the pitches in the piece using the two half step, one letter name process.