Is it possible to estimate road grade while riding? It would be nice to be able to estimate the grade of a road while riding, even if the estimate is not completely accurate. With a GPS, in theory it should be possible in theory to ride a short distance and divide the difference in elevation by the distance ridden to get a rough estimate. (Note that the sine and tangent are comparable for small angles.)

Is the elevation given by a cell phone or GPS-equipped bike computer accurate enough to give a meaningful grade estimate over short distances? Furthermore, is there any practical way to estimate the grade of a road that does not require a GPS?
Get an inclinometer.  They're not particularly accurate, but readout is instant and the price is right.