TBLFM insert new row with current time

The following line inserts a new row, but with the content of cell 1 "#ERROR".

#+TBLFM: @2$1='(let ((org-table-fix-formulas-confirm 0)) (org-table-insert-row)) 

The part with setting org-table-fix-formulas-confirm to 0 is so that it doesn't update all the indices in the formulae.

So using two formulae, the following works:

| date | start | end | |------------------+-------+-------| | [2016-08-01 Mon] | 08:00 | 16:00 | |------------------+-------+-------| #+TBLFM: @2$1='(let ((org-table-fix-formulas-confirm 0)) (org-table-insert-row)) #+TBLFM: @2$1='(format-time-string "[%Y-%m-%d %a]")::@2$2='(format-time-string "%H:%M") #+TBLFM: @2$3='(format-time-string "%H:%M") 

Note: My answer is derived directly from Pål GD's great answer. I only figured out how to prevent the #ERROR message.

Call the elisp functions inside let declaration section and return the date string.

Like this

(let ((org-table-fix-formulas-confirm 0) (x (format-time-string "[%Y-%m-%d %a]")) (y (org-table-insert-row))) x)

Below is complete example for your answer code

| date | start | end | |------------------+-------+-------| | [2020-08-12 Wed] | 09:10 | 09:10 | | [2016-08-01 Mon] | 08:00 | 16:00 | |------------------+-------+-------| #+TBLFM: @3$1='(let ((org-table-fix-formulas-confirm 0) (x (format-time-string "[%Y-%m-%d %a]")) (y (org-table-insert-row))) x)::@3$2='(format-time-string "%H:%M")::@3$3='(format-time-string "%H:%M") 

Thank you for asking this question!

This answer was tested using:

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emacs version: GNU Emacs 25.2.1 (x86_64-unknown-cygwin, GTK+ Version 3.22.10)
org-mode version: Org mode version 9.1.2