A pre-money valuation means the valuation of your startup without taking into account the money you are about to raise (i.e. what it is worth today before any funding).
The Capitalisation Definition is used to calculate the price per share that will be used when the SAFE converts to share if the SAFE converts using the valuation cap. A pre-money SAFE does not include the shares given to convertibles in the “Capitalisation Definition”.
A SAFE is essentially an agreement between an investor and your company where the investor gives you money now for a good deal in the future when you sell shares to other investors at a specific price.
The deal is based either on a discount on the price per shares that others will be paying, or a price per share calculated by using the valuation cap and the capitalisation definition. The “discount”, “valuation cap” and “capitalisation definition” are all terms you can find in the SAFE document.
Pre-money SAFEs have a standard definition used for the “capitalisation definition”. You can determine if your SAFE is pre-money by looking at the title of the SAFE for the words “pre-money” or you can look for the “capitalisation definition” term. If the capitalisation definition does NOT have any reference to “other converting securities” or “SAFEs” or “convertibles”, then it is a pre-money SAFE. Pre-money SAFEs that convert using the valuation cap will be diluted by other convertibles that your company has.