Area Between Two Curves Calculator
Area enclosed between two polynomial curves.
Enter your values
Enter the f: x^2 coeff you are working with.
Enter the f: x coeff you are working with.
Enter the f: constant you are working with.
Enter the g: x^2 coeff you are working with.
Enter the g: x coeff you are working with.
Enter the g: constant you are working with.
Enter the lower bound you are working with.
Enter the upper bound you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Area enclosed between two polynomial curves. |
|---|---|
| Category | Math |
| Inputs needed | f: x^2 coeff, f: x coeff, f: constant, g: x^2 coeff, g: x coeff, g: constant, Lower bound, Upper bound |
| Main output | Signed area |
| Formula | Area = ∫[a,b] (f(x)-g(x)) dx |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- f: x^2 coeff
- Enter the f: x^2 coeff you are working with.
- f: x coeff
- Enter the f: x coeff you are working with.
- f: constant
- Enter the f: constant you are working with.
- g: x^2 coeff
- Enter the g: x^2 coeff you are working with.
- g: x coeff
- Enter the g: x coeff you are working with.
- g: constant
- Enter the g: constant you are working with.
- Lower bound
- Enter the lower bound you are working with.
- Upper bound
- Enter the upper bound you are working with.
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.
What do I need to enter into the Area Between Two Curves Calculator?
Just 8 values: f: x^2 coeff, f: x coeff, f: constant, g: x^2 coeff, g: x coeff, g: constant, lower bound, upper bound. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Area Between Two Curves Calculator work out the answer?
The area between two curves is the definite integral of the top curve minus the bottom curve, taking the absolute value if needed. It applies the formula Area = ∫[a,b] (f(x)-g(x)) dx and shows the working so you can check each step by hand.
Is the Area Between Two Curves Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.