Both of these adjectives are based on the noun proportion.
The noun proportion can mean “a part, portion, amount, or percentage” of something. For example, “He miscalculated the proportion of water to alcohol in the solution.”
Proportion can also refer to a balance between two things. For example, “The king rewarded the knight in proportion to his merit.”
Outside certain scientific contexts, the words tend to be used interchangeably. Both mean “in proportion.” Nevertheless, some speakers perceive a difference between proportional in reference to “amount or percentage” and proportionate to mean “comparable, equivalent, or analogous.”
The US Senate would be proportional in terms of the US population if it were made up of 50 men and 50 women.
When someone initiates an attack against you, a proportionate response will be one that equals but does not exceed the original attack in severity.
Here are some recent examples from the Web:
Benin’s Military Manual (1955) requires respect for the principle of proportionality. According to the manual, “a military action is proportionate if it does not cause loss or damage to civilians which is excessive in relation to the expected overall result.”
A windmill’s noise is directly proportional to the speed of its rotor tips.
Your proportionate share of production from a well is calculated based on the net acres you own in the spacing unit.
Unlike a real roulette wheel the sections are different sizes, proportional to the individual’s fitness, such that the fittest candidate has the biggest slice of the wheel and the weakest candidate has the smallest.
The adverbs for proportionate and proportional are proportionately and proportionally.