Degree and Leading Coefficient Calculator
Type in a polynomial and instantly find its degree, leading term, and leading coefficient.
How to use this calculator
Type your polynomial into the field using ^ for exponents, for example 5x^7 + 2x^5 - 4x^3 + x^2 + 15. Stick to one variable per polynomial. Press Calculate to see the degree, leading coefficient, and leading term, or Reset to clear the field.
What are degree, leading term, and leading coefficient?
The degree of a polynomial is the highest exponent that appears on its variable. It tells you the polynomial's overall shape — a degree-2 polynomial is a parabola, a degree-3 polynomial is a cubic curve, and so on.
The leading term is the term that holds that highest exponent. The leading coefficient is just the number multiplying that term. Together, the leading term dominates the polynomial's behavior for very large or very small values of x, which is why it's the first thing to identify when analyzing a polynomial's end behavior.
How to find the degree and leading coefficient
2. Find the term with the largest exponent — that exponent is the degree.
3. The coefficient of that term is the leading coefficient.
4. The full term (coefficient and variable together) is the leading term.
Worked example
The highest exponent present is 7, so the degree is 7. The term with that exponent is 5x⁷, so the leading term is 5x⁷ and the leading coefficient is 5.
Frequently asked questions
What if the polynomial isn't written in order?
It doesn't matter what order the terms are in — the calculator compares every exponent and picks out the highest one automatically.
What's the degree of a constant, like 15?
A nonzero constant has degree 0, since it can be thought of as 15x⁰.
Can the leading coefficient be negative?
Yes. If the term with the highest exponent has a minus sign in front of it, the leading coefficient is negative, and that affects the polynomial's end behavior.
Does this work with more than one variable?
No, this calculator is built for single-variable polynomials, like ones written only in x. Multivariable polynomials define degree differently.