5.8309
um
5,830.9
nm
51.4144
THz
0.212633
eV
20.516
kJ/mol
19.4498
fs
0
cm^-1
0
cm^-1
0
1=yes, 0=no
0
cm^-1
5.8309
um
5,830.9
nm
51.4144
THz
0.212633
eV
20.516
kJ/mol
19.4498
fs
0
cm^-1
0
cm^-1
0
1=yes, 0=no
0
cm^-1
The IR Spectrum Calculator converts infrared wavenumber values to wavelength, frequency, and energy, while also providing a functional group correlation lookup. Infrared spectroscopy is one of the most widely used techniques in organic chemistry, polymer science, forensic analysis, and quality control. In an IR spectrum, absorption peaks at specific wavenumbers correspond to molecular vibrations — stretching and bending of chemical bonds. This calculator helps identify which functional group is responsible for an observed absorption by comparing the wavenumber with characteristic ranges. It also converts between the wavenumber (cm⁻¹), wavelength (μm), and frequency (THz) representations, enabling cross-referencing with different spectroscopic databases and instrument formats. Whether you are interpreting an FTIR spectrum or preparing for a spectroscopy exam, this tool provides the essential conversions and reference data.
The conversion from wavenumber to wavelength uses the reciprocal relationship:
$$\lambda (\mu\text{m}) = \frac{10000}{\tilde{\nu} (\text{cm}^{-1})}$$
Frequency is obtained from: $$f = c \cdot \tilde{\nu} = \frac{c}{\lambda}$$
And photon energy from: $$E = hc\tilde{\nu} = \frac{hc}{\lambda}$$
The functional group correlation table maps observed wavenumbers to likely bond types based on established reference data. Key regions of the IR spectrum include:
$$\text{4000-2500 cm}^{-1}: \text{X-H stretching (O-H, N-H, C-H)}$$
$$\text{2500-2000 cm}^{-1}: \text{Triple bond stretching (C≡C, C≡N)}$$
$$\text{2000-1500 cm}^{-1}: \text{Double bond stretching (C=O, C=C, C=N)}$$
$$\text{1500-400 cm}^{-1}: \text{Fingerprint region (C-O, C-N, bending modes)}$$
Each IR absorption band has a characteristic position (wavenumber), intensity (strong, medium, weak), and shape (broad, sharp). The position tells you what type of bond is vibrating. The intensity relates to the change in dipole moment during the vibration — more polar bonds give stronger absorptions. The shape can indicate hydrogen bonding (broad O-H) or crystallinity. Use the functional group lookup to narrow down possible assignments, then consider the overall molecular context. Remember that the fingerprint region (below 1500 cm⁻¹) is unique to each molecule and is best used for identification by matching against reference databases.
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A strong absorption at 1715 cm⁻¹ falls within the ketone C=O stretch range (1705–1725 cm⁻¹). This is one of the most easily recognizable bands in IR spectroscopy due to its intensity and narrow position range.
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A broad absorption centered at 3400 cm⁻¹ is characteristic of hydrogen-bonded O-H stretching in alcohols. The breadth of this band reflects the distribution of hydrogen bond strengths and lengths in the liquid phase.
In liquids and solutions, O-H groups participate in extensive hydrogen bonding. Each O-H bond has a slightly different hydrogen bond environment, resulting in a continuous range of slightly different vibrational frequencies. This ensemble of frequencies produces the characteristically broad absorption between 3200–3600 cm⁻¹.
C=O stretching frequencies vary systematically: amides (1630–1690 cm⁻¹) < acids (1700–1725 cm⁻¹) < ketones (1705–1725 cm⁻¹) < aldehydes (1720–1740 cm⁻¹) < esters (1735–1750 cm⁻¹) < acid chlorides (1770–1815 cm⁻¹) < anhydrides (1800–1850 cm⁻¹). Conjugation lowers the frequency, while electron-withdrawing groups raise it.
The region below 1500 cm⁻¹ is called the fingerprint region because the complex pattern of absorption bands is unique to each molecule. It contains C-C, C-O, C-N stretching and various bending modes. This region is primarily used for compound identification by spectral matching rather than functional group analysis.
Bond stretching frequency depends on bond strength and atomic masses: ν̃ ∝ √(k/μ), where k is the force constant and μ is the reduced mass. Triple bonds are stronger than double bonds (higher k), resulting in higher vibrational frequencies. C≡C absorbs near 2100–2260 cm⁻¹, while C=C absorbs near 1620–1680 cm⁻¹.
Yes. Using Beer's law (A = εlc) applied to a specific absorption band, concentrations can be determined. FTIR instruments with their excellent frequency reproducibility are particularly suited for quantitative work. However, band overlap and matrix effects can complicate quantitative IR analysis compared to UV-Vis.
Dispersive IR instruments use a monochromator to scan through wavelengths sequentially. FTIR uses an interferometer to measure all wavelengths simultaneously, offering major advantages: higher signal-to-noise ratio (Fellgett's advantage), better wavelength accuracy (Connes' advantage), higher throughput (Jacquinot's advantage), and faster acquisition. FTIR has largely replaced dispersive instruments.
A molecular vibration is IR-active only if it causes a change in dipole moment. Symmetric vibrations of homonuclear molecules (like the symmetric stretch of CO₂ or the vibrations of N₂, O₂) produce no dipole change and are therefore IR-inactive. These vibrations may be Raman-active instead (complementary selection rules).
Attenuated Total Reflectance (ATR) measures IR absorption by pressing the sample against a crystal with high refractive index. The IR beam undergoes total internal reflection, and the evanescent wave penetrates ~0.5–5 μm into the sample. ATR requires minimal sample preparation and works with solids, liquids, and pastes, making it the most convenient sampling method for routine analysis.
In the simple harmonic oscillator model, the vibrational frequency is: ν̃ = (1/2πc)√(k/μ), where k is the force constant (bond stiffness in N/m) and μ is the reduced mass (μ = m₁m₂/(m₁+m₂)). Stronger bonds and lighter atoms give higher frequencies. This model explains the general trends but not the exact positions of IR bands.
A nonlinear molecule with N atoms has 3N-6 vibrational modes. A linear molecule has 3N-5 modes. For example, water (3 atoms, nonlinear) has 3 modes: symmetric stretch, asymmetric stretch, and bend. Not all modes are necessarily IR-active, and some may be degenerate (same frequency).
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