S(x)
-
C(x)
-
S(x) = ∫₀ˣ sin(πt²/2) dt
C(x) = ∫₀ˣ cos(πt²/2) dt
How to Use
Enter a value of x and the tool computes the Fresnel sine integral S(x) and cosine integral C(x) using high-precision numerical integration. Fresnel integrals describe near-field diffraction and also define the clothoid (Euler spiral) used in road and railway transition curves, so the calculator serves both optics work and civil-engineering study.
- Fresnel sine integral S(x)
- Fresnel cosine integral C(x)
- High-precision numerical integration
- Instant results as you type
- Definition formulas shown alongside results
Use cases
- Diffraction calculations in optics
- Clothoid (transition curve) work in road and rail design
- Electromagnetic wave propagation problems
- Checking homework in mathematical physics