Cycle highway should be usable by cyclists with different levels of fitness and skill and on different types of bicycles. Not all cyclists are sporty, not all bicycles have a wide range of gears, therefore not everyone is able to climb steep hills.
Way downhill might seem easier, but with steep gradients it can be risky, due to higher speeds and much longer braking distance (gravity is counteracting the braking power).
Overall elevation changes increase the energy expense of cyclists, therefore reducing the comfort of using and competitiveness of cycle highway.
The simplest measure of gradient is percentage – rise/run. E.g. a gradient of 3% means that the cyclist ascends or descends 3 m in 100 m. G=H/L
But steepness is not everything – short steep slopes can be acceptable, provided that the cyclists have space to speed up before climbing it (and – going in the opposite direction – naturally slow down without braking after descending). Several manuals vary the threshold for steepness depending on slope length or height difference. CROW’s “Design manual for bicycle traffic” introduced a measure of slope severity S=H2/L.
A somewhat related parameter is vertical curve radius. The higher the radius, the smoother the transition between sections of the cycle path with different gradients.
Minimum and recommended values
Ad 1. Gradient for cyclists should not generally exceed 6%, although very short sections with up to 10% might be acceptable. For longer ascends gradients should be reduced to 2-3% (but see also the discussion further).
Ad 2. Recommended S = 0.075, max S < 0.200.
Ad 3. Qualitätsstandards für Radschnellverbindungen (Baden-Württemberg) require a radius of at least 50 m for concave curves and 80 m for convex curves.
Guidelines/ standard
Maximum gradients
Design Manual for Bicycle Traffic (CROW, NL)
2-10% depending on slope height - see slope severity
Qualitätsstandards für Radschnellverbindungen (Baden-Württemberg, D)
6%
Réseau cyclable à haut niveau de service. Objectifs et principes d'aménagement (CEREMA, F)
6%
Manual for the design of cyclepaths in Catalonia (E)
2% (no length limit); 4% (max 4 km); 5% (2 km); 6% (240 m); 10% (30 m); 25% (15 m)
How is it related to other criteria?
Design speed and parameters related to it should be increased on slopes, both because of higher speed and reduced braking capabilities for the cyclists going downhill.
Gradients can be a critical risk factor for crossings on slopes and shortly after the bottom of them. Cyclists going downhill have less time to react and require significantly longer distances to stop.
Width should be increased on slopes – cyclists going downhill appreciate wider safety margin because of higher speed, and those going uphill need more space for balancing the bike because of lower speed.
If you need to overcome a significant elevation difference, achieving low gradients can compromise directness.
The countries, where the most advanced cycle infrastructure design guidelines come from, are mostly flat, which makes it feasible to put very strict requirements on gradients and slope severity. It is still an open question whether such requirements can be adopted everywhere. E.g. the Dutch do not have much experience with the design of cycle infrastructure in mountainous or even hilly areas. There are some ideas that can alleviate the high elevation differences, such as various types of bicycle lifts, combination with public transport or support for electric bikes, but they are not yet integrated in the established cycle highway standards and guidelines.
Slopes and gradients 
Ramp on the cycle highway F261 in Waalwijk, Netherlands. 
