Context : Carbon rich objects represent an important phase during the late stages of evolution of low and intermediate mass stars .
They contribute significantly to the chemical enrichment and to the infrared light of galaxies .
A proper description of their atmospheres is crucial for the determination of fundamental parameters such as effective temperature or mass loss rate .

Aims : We study the spectroscopic and photometric properties of carbon stars .
In the first paper of this series we focus on objects that can be described by hydrostatic models neglecting dynamical phenomena like pulsation and mass loss .
As a consequence , the reddening due to circumstellar dust is not included .
Our results are collected in a database , which can be used in conjunction with stellar evolution and population synthesis calculations involving the AGB .

Methods : We have computed a grid of 746 spherically symmetric COMARCS atmospheres covering effective temperatures between 2400 and 4000 K , surface gravities from log ( g~ { } [ cm / s ^ { 2 } ] ) = 0.0 to -1.0 , metallicities ranging from the solar value down to one tenth of it and C/O ratios in the interval between 1.05 and 5.0 .
Subsequently , we used these models to create synthetic low resolution spectra and photometric data for a large number of filter systems .
The tables including the results are electronically available .
First tests of the application on stellar evolution calculations are shown .

Results : We have selected some of the most commonly used colours in order to discuss their behaviour as a function of the stellar parameters .
A comparison with measured data shows that down to 2800 K the agreement between predictions and observations of carbon stars is good and our results may be used to determine quantities like the effective temperature .
Below this limit the synthetic colours are much too blue .
The obvious reason for these problems is the neglect of circumstellar reddening and structural changes due to pulsation and mass loss .

Conclusions : The warmer carbon stars with weak pulsation can be successfully described by our hydrostatic models .
In order to include also the cooler objects with intense variations , at least a proper treatment of the reddening caused by the dusty envelopes is needed .
This will be the topic of the second paper of this series .