Corporate Captain reported third party vendor TOLD software is missing runway slope option which may compute inaccurate TOLD data.

Narrative

Due to the longer runway being closed at SHR; we were forced to use RW06/24 for departure. While mission planning for our fuel load; we ran APG (Aircraft Performance Group) software for the shorter runway and noticed that there was only a very small difference between the takeoff distances of the two runways. This surprised me because there is a 1.6% slope on that runway (uphill for RW24; downhill for RW06).So; the other pilot and I used our FMSCDU (Flight Management System Control Display Unit) to calculate the takeoff distance and noticed that for the runway data no slope was given. This is an FAA approved system and extremely common (Collins ProLine 21 Advanced). We manually input the runway slope for RW24; which put our takeoff distance well beyond takeoff distance available even without fuel or passengers. There was a Part 135 operator who was in the FBO who was relying on third party data to takeoff rather than the FMSCDU; which begs the question of whether the third party provider was aware of the slope. Fortunately; we were able to takeoff on RW06; which had the beneficial downhill slope.We also checked the FMSCDU for other runways we commonly use that have slopes. None of these runways had the slopes in the database; which means that the TOLD (Takeoff and Landing Data) for the uphill runways is inaccurate and possibly out of range for legal operations.Also; I think third party data providers need to be aware that they may not have the requisite information regarding runway slopes.We were able to find the slopes in ForeFlight. The FAA VFR Sup for SHR doesn't list the slope for RW06/24 individually.