Calculator
Enter a frequency (f) or an angular frequency (ω). The calculator converts units, computes photon energy, and provides common energy scales for science work.
Formula Used
Photon energy is proportional to frequency:
- E = h × f, where E is energy (J), h is Planck’s constant, and f is frequency (Hz).
- If using angular frequency: f = ω / (2π), with ω in rad/s.
- Energy in electronvolts: E(eV) = E(J) / e, where e is the elementary charge.
- Optional wavelength link: λ = c / f, where c is the speed of light.
Constants used: h = 6.62607015×10⁻³⁴ J·s, c = 299792458 m/s, e = 1.602176634×10⁻¹⁹ J per eV.
How to Use This Calculator
- Select whether your input is frequency (f) or angular frequency (ω).
- Enter the value and choose the matching unit scale.
- Pick a primary output unit and set precision.
- Click Calculate to display results above the form.
- Use the CSV or PDF buttons to download your result table.
Example Data Table
These examples show typical photon energies across frequency ranges.
| Frequency | Energy (J) | Energy (eV) | Approx. wavelength |
|---|---|---|---|
| 100 MHz | 6.626×10⁻²⁶ | 4.136×10⁻⁷ | ≈ 3.00 m |
| 2.45 GHz | 1.624×10⁻²⁴ | 1.014×10⁻⁵ | ≈ 0.122 m |
| 500 THz | 3.313×10⁻¹⁹ | 2.067 | ≈ 600 nm |
| 2.42 PHz | 1.603×10⁻¹⁸ | 10.00 | ≈ 124 nm |
Photon Energy from Frequency: Practical Guide
1) Why frequency controls photon energy
Photon energy scales directly with frequency. A 100 MHz radio photon carries about 6.626×10−26 J, while 500 THz light carries about 3.313×10−19 J. That difference is roughly seven orders of magnitude. When you compare signals across bands, this linear scaling is the key reason energies change so dramatically.
2) Constants and trustworthy conversions
The calculator uses modern SI definitions: Planck’s constant h = 6.62607015×10−34 J·s and the elementary charge e = 1.602176634×10−19 J per eV are exact. Converting through these constants keeps results consistent when you switch between joules and electronvolts, and when you report keV, MeV, or GeV for higher-energy work.
3) Frequency versus angular frequency ω
Some domains, especially oscillators and differential-equation models, describe signals using angular frequency ω in rad/s. Photon energy still depends on linear frequency f in Hz, so the tool converts using f = ω/(2π). For instance, ω = 6.283×109 rad/s corresponds to f ≈ 1.0 GHz. Selecting the correct input type prevents a systematic 2π error in energy.
4) Interpreting values across the spectrum
Visible photons typically fall around 1.6–3.3 eV (about 400–750 nm). Ultraviolet can exceed 10 eV, and X‑rays often sit in the keV range. At the other end, microwaves near 2.45 GHz produce about 1.01×10−5 eV per photon, which is why microwave heating is a bulk, many-photon process rather than single-photon chemistry.
5) Wavelength output for rapid sanity checks
To help you validate entries, the calculator also estimates wavelength with λ = c/f using c = 299792458 m/s. A 500 THz input returns ≈ 600 nm, aligning with orange‑red light. If your wavelength seems implausible, first confirm the unit prefix (MHz vs GHz vs THz), then confirm whether the input is f or ω.
6) Precision settings and numerical stability
Because energies can be extremely small or very large, scientific notation is used when needed to preserve significant figures. Set the precision to match your measurement quality; extra digits do not add physical certainty. For comparisons across runs, keep the same precision so differences reflect physics rather than formatting.
7) Professional workflow: validate, document, and export
Before using results in reports, compare your input against the example table to catch order‑of‑magnitude mistakes. Document the input value, unit prefix, and whether you used f or ω. Then export CSV for spreadsheets and batch studies, or PDF for lab notebooks and reviews. The exported table includes multiple energy scales plus wavelength, which improves clarity when collaborating across optics, electronics, and radiation teams.
FAQs
1) What frequency range can I use here?
Any positive value is accepted with prefixes from Hz to PHz, and rad/s up to Trad/s. Very large or tiny results are shown in scientific notation for readability.
2) Should I enter frequency or angular frequency?
Use frequency for Hz-based inputs (cycles per second). Use angular frequency for rad/s. The calculator converts ω to f using f = ω/(2π) automatically.
3) Why show joules and electronvolts together?
Joules are the SI standard, while electronvolts are common in atomic, optical, and radiation work. Displaying both removes conversion friction and improves interpretation.
4) How is wavelength computed?
Wavelength is calculated from linear frequency using λ = c/f with c = 299792458 m/s. It is provided as a cross-check and for quick band identification.
5) Why does the output use “e” notation?
Photon energies can be extremely small in RF and much larger at high frequencies. Scientific notation avoids long strings of zeros and preserves significant figures.
6) Can I use this relation for mechanical waves?
No. E = h f is for photons of electromagnetic radiation. Mechanical waves do not have photon energy. For particles, use the correct quantum relations.
7) What details should I record in a report?
Record the input value, unit and prefix, whether you used f or ω, and the displayed energy unit. Including wavelength and an alternate unit improves reproducibility.