When saying shma in davening without a minyan, the three words א-ל מלך נאמן are recited. It is done in order to make up 248 words total (with a minyan, the chazzan says ה' א-לוקיכם אמת to get the 3).
With this in mind, what is considered davening alone that kel melech ne'eman would be said?
Must you be actually without a minyan, or can you be considered 'alone' even if you're with a minyan, but catching up? Does it make a difference if the chazzan hasn't finished saying shma yet or not?
בִּקְרִיאַת שְׁמַע יֵשׁ רמ''ה תֵּבוֹת, וּכְדֵי לְהַשְׁלִים רמ''ח כְּנֶגֶד אֵיבָרָיו שֶׁל אָדָם, מְסַיֵּם שְׁלִיחַ צִבּוּר (ב) ה' אֱלֹקיכֶם אֱמֶת, וְחוֹזֵר וְאוֹמֵר בְּקוֹל רָם ה' אֱלֹהֵיכֶם אֱמֶת:
In shema there are 245 words, and in order to get to 248 words (corresponding to the number of bones in a human body), the prayer leader says "ה' אלוקיכם אמת," by himself, and then repeats it out loud (so that it will count for the congregation).
Rama, there:
וְיֵשׁ שֶׁכָּתְבוּ דְּכָל הַקּוֹרֵא קְרִיאַת שְׁמַע בְּיָחִיד, יֹאמַר קל מֶלֶךְ נֶאֱמָן (ה) שְׁמַע וְגו', כִּי ג' תֵּבוֹת אֵלּוּ מַשְׁלִימִים הַמִּנְיָן שֶׁל רמ''ח....וְנִרְאֶה לִי מִכָּל מָקוֹם כְּשֶׁקּוֹרֵא עִם הַצִּבּוּר, לֹא יֹאמַר קל מֶלֶךְ נֶאֱמָן, רַק יֹאמַר אָמֵן אַחַר הַשְּׁלִיחַ צִבּוּר כְּשֶׁמְּסַיֵּם הַבְּרָכָה, וְכֵן נוֹהֲגִין, וְנָכוֹן הוּא.
Some have written that anyone who reads שמע by himself should say "קל מלך נאמן," so that these three words will round out שמע to 248 words....I would say that when someone is with a congregation, he should only say אמן (because קל מלך נאמן might replace that אמן right before שמע) -- this is what is done, and it is correct.
My reading of the above is that קל מלך נאמן is not said when one is with a minyan, where the חזן says ה' אלוקיכם אמת, and is said in every other case -- hence "alone" means where the חזן will not say ה' אלוקיכם אמת before the end of your שמע.
