Area Between Two Curves Calculator
Area enclosed between two polynomial curves.
Enter your values
ⓘ Live results
Results
- Signed area
- 10.666667
- Absolute area
- 10.666667
- Difference function
- -1x^2 + 0x + 4
Quick answer
The area between two curves is the definite integral of the top curve minus the bottom curve, taking the absolute value if needed.
Area = ∫[a,b] (f(x)-g(x)) dx
How to use the Area Between Two Curves Calculator
- 1Enter the coefficients of curve f(x) and curve g(x).
- 2Enter the interval [lower, upper] over which to find the area.
- 3The tool integrates f(x)-g(x) over that interval.
Worked example
Using the values the calculator loads with:
Inputs
- f: x^2 coeff0
- f: x coeff0
- f: constant4
- g: x^2 coeff1
- g: x coeff0
- g: constant0
- Lower bound-2
- Upper bound2
Results
- Signed area10.666667
- Absolute area10.666667
- Difference function-1x^2 + 0x + 4
Frequently asked questions
What if curves cross inside the interval?
The signed area may cancel; split the interval at the crossing point(s) and add absolute areas for the true enclosed area.
Which curve should be f?
Order doesn't matter — a negative result just means g was above f on average.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.