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agreeable to reason; reasonable; sensible:
a rational plan for economic development.
having or exercising reason, sound judgment, or good sense:
a calm and rational negotiator.
being in or characterized by full possession of one’s reason; sane; lucid:
The patient appeared perfectly rational.
endowed with the faculty of reason:
rational beings.
of, relating to, or constituting reasoning powers:
the rational faculty.
proceeding or derived from reason or based on reasoning:
a rational explanation.
Mathematics.

capable of being expressed exactly by a ratio of two integers.
(of a function) capable of being expressed exactly by a ratio of two polynomials.

Classical Prosody. capable of measurement in terms of the metrical unit or mora.
Mathematics, .
Contemporary Examples

Any rational discussion of what Obama and his party need to do must begin with this existential question: What the hell happened?
How to Stop the Bleeding Howard Kurtz November 3, 2010

The idea was to create such pressure on Congress that a Super Committee would forge a rational plan.
Romney’s Defense Argument Misfires Howard Kurtz July 23, 2012

David Frum calls upon the GOP’s rational caucus to step up before it’s too late.
Will the Republican Moderates Please Stand Up? David Frum October 9, 2013

Police said she appeared to be “disoriented and confused and not rational and paranoid.”
Shannan Gilbert Body Likely Found, New York Police Say Christine Pelisek December 12, 2011

In other words, our rational sides are simply not equipped to make complex and far-reaching decisions like when to get married.
The Science of When to Get Married Hannah Seligson April 6, 2009

Historical Examples

Though he had no rational reason for expecting trouble he had still his hunch and his intuition.
The Blind Spot Austin Hall

Be rational, and just, and calm, and tell me whose idea was that.’
Life And Adventures Of Martin Chuzzlewit Charles Dickens

We are experiencing in the world-war a fearful balancing-up with the rational intentionality of organised culture.
Collected Papers on Analytical Psychology C. G. Jung

And don’t trust him at any time; for when he seems most rational, he’s wildest in his talk.
Life And Adventures Of Martin Chuzzlewit Charles Dickens

The natural turn of his temper inclined him to rational society, but in that his wife could bear no part.
A Description of Millenium Hall Sarah Scott

adjective
using reason or logic in thinking out a problem
in accordance with the principles of logic or reason; reasonable
of sound mind; sane: the patient seemed quite rational
endowed with the capacity to reason; capable of logical thought: man is a rational being
(maths) expressible as a ratio of two integers or polynomials: a rational number; a rational function
noun
(maths) a rational number
adj.

late 14c., “pertaining to reason;” mid-15c., “endowed with reason,” from Old French racionel and directly from Latin rationalis “of or belonging to reason, reasonable,” from ratio (genitive rationis) “reckoning, calculation, reason” (see ratio).

rational ra·tion·al (rāsh’ə-nəl)
adj.

Having or exercising the ability to reason.

Influenced by reasoning rather than by emotion.

Of sound mind; sane.

Based on scientific knowledge or theory rather than practical observation.

[Mathematics] a fractional number n/d, where n and d are integers, n is the numerator and d is the denominator. The set of all rational numbers is usually called Q. Computers do not usually deal with rational numbers but instead convert them to real numbers which are represented (approximately in some cases) as floating-point numbers. Compare irrational.