Compost has nutrients in it, but they are not present in the variety and quantity to justify using it as a replacement for a general, balanced all-purpose fertilizer. Furthermore, it does not offer nutrients directly to plants. It provides food to sustain the billions of microorganisms in the soil so that they are able to go about the business of transforming the soluble compounds in the compost into a form that can then be absorbed by the roots of plants. The many oxygen containing compounds in compost bring oxygen to these micro bugs which is essential to their reproduction. As compost is created by means of the decomposition of whatever organic materials happen to be dumped on the pile, certain acids are formed as byproducts. These acids help to break down some of the rock particles in the soil, releasing nutrients to the plants that would otherwise not be available to them.
When compost is fresh, newly made, and rain has not had an opportunity to leach its nutrients from it, it holds nitrogen, some phosphorous, some potassium, and many of the trace minerals needed by landscape plants during the growing season. Compost that has been left out in the weather--or even stored covered for more than 6 months--has probably lost much of the nitrogen, phosphorous, and potassium to released gases, but still retains many of the micronutrients that are so beneficial to the plants. About half of the nutrients that are present in compost are released for plant use during the first year. Half of those nutrients that are left are released during the second year, and so on after that.
Adding compost to yard and garden soil improves its overall fertility and cures some soil mineral deficiencies. However, do not use it as a replacement for an annual application of general purpose slow-release nitrogen fertilizer in and around the entire landscape each year. Most ornamental plants require about 1/2 pound to one pound of nitrogen per 100 square feet of garden. Trees require only about .2 to .3 pounds of nitrogen for every 100 square feet of root area. Flowers and vegetables, while short lived, have a higher level of need than do the long living woody plants.
The amount of nitrogen in a given batch of finished compost is not terribly predictable. It depends on the raw materials used, the C/N ratio of the pile, how often the pile was turned, and whether any amendments were added--just to name a few variables. For example, compost made from hay is higher in nitrogen than compost made from straw. Leaves have about half the nitrogen that manure has. For comparison, aged cow manure is about 1.4% nitrogen and aged chicken manure is about 2.8% nitrogen. Here again, any kind of fine tuning is problematical.
Taking into consideration all the unknowns, it is fair to say that if your compost is made of leaves and grass it will probably have about 0.8 to 2% nitrogen, averaging about 1% in most cases. That percentage is sufficient to yield about .6 pounds of nitrogen if 1 inch of compost is spread over 100 square feet of garden or lawn area, enough for most trees and shrubs, but not necessarily enough for annual plants. A fresh compost, which will have a relatively high nitrogen content, may itself provide enough nutrition to a flower bed, although some supplementary foliar feeding later in the season may be wise as insurance. Because it is not likely that you would have enough compost to enable you to put 1 inch of compost over an entire mature lawn, settle for a 1/4 layer. This will provide some nutrients to the lawn grass, which you can supplement with an annual fall or spring application of slow release granulated fertilizer.