The photoelectric effect calculator above applies Einstein's photoelectric equation to a metal surface and a beam of light. It returns the largest kinetic energy any emitted electron can carry, the voltage that would just stop those electrons reaching a collector, the longest wavelength that can cause emission at all, and the speed of the fastest electron. When the light is too red to eject anything, it says so plainly rather than handing back a negative number.
Arb Digital builds free physics calculators that treat the boundaries of a phenomenon as part of the answer. The threshold in the photoelectric effect is not a rounding artefact; it is the single observation that classical wave physics could not explain and that forced photons into existence.
What This Photoelectric Effect Calculator Does
You supply a work function, either by choosing a metal or by typing a value, and describe the incident light as a wavelength, a frequency or a photon energy. Any one of the three determines the other two, and the tool shows all of them.
The headline is the maximum kinetic energy of an emitted electron, in electronvolts, with the joule equivalent underneath. It is a maximum rather than a typical value because electrons deeper inside the metal must spend more than the minimum escape energy on the way out, so real emitted electrons form a spread running from zero up to this ceiling.
The stopping voltage is that ceiling expressed as a potential. Apply it in reverse across the gap and even the fastest electron is turned back just before it arrives, so the photocurrent falls to zero. The threshold wavelength is the longest wavelength that still ejects anything: at exactly that wavelength an electron just escapes with no energy left over. The fastest electron speed is the non-relativistic speed corresponding to the maximum kinetic energy, and the tool warns you when that approximation starts to strain.
How to Use It
- Set the work function first. It belongs to the surface, not to the light. Choosing a metal fills the field; typing over it lets you use a measured value, which is always better than a table.
- Describe the light in whichever unit you have. Laser sources are usually quoted in nanometres, spectroscopy in electronvolts, radio-adjacent work in frequency. They are interchangeable here.
- Compare the photon energy with the work function. If the photon carries less, nothing is emitted and no amount of intensity changes that. The tool states this outcome rather than continuing.
- Read the stopping voltage as the measurable quantity. In a real experiment you do not measure electron energies directly; you find the retarding voltage that kills the current, which is the same number.
- Check the threshold wavelength when choosing a source. It tells you immediately whether a green laser, a blue LED or a UV lamp is needed for a given metal.
The Formula: Einstein's Photoelectric Equation
A photon carries energy E = hf, where h is the Planck constant and f is the frequency. Since f = c ÷ λ, the same energy in terms of wavelength is E = hc ÷ λ. Expressed in the units used here, hc is 1,239.84 eV·nm, so photon energy in electronvolts is simply 1,239.84 divided by the wavelength in nanometres.
One photon interacts with one electron and gives it everything. Some of that goes on escaping the surface, which costs the work function φ, and whatever remains becomes kinetic energy: Kmax = hf − φ. Setting Kmax to zero gives the threshold frequency fc = φ ÷ h, which depends only on the metal. The stopping voltage follows from Kmax = eΔVs, so in electronvolts the two are numerically identical. OpenStax University Physics Volume 3, section 6.2 on the photoelectric effect, sets out all four relationships and the experiment behind them.
The constants are fixed by definition. The Planck constant is exactly 6.626 070 15 × 10−34 J·Hz−1 and carries no uncertainty at all, as recorded in the NIST reference on constants, units and uncertainty entry for the Planck constant. That is because the 2019 redefinition of the SI fixed its value and defined the kilogram from it, rather than measuring it against a kilogram.
Work the defaults through. Sodium, φ = 2.46 eV, lit at 400 nm. Photon energy = 1,239.84 ÷ 400 = 3.100 eV. Subtract the work function: Kmax = 3.100 − 2.46 = 0.640 eV, so the stopping voltage is 0.640 V. The threshold wavelength is 1,239.84 ÷ 2.46 = 504 nm, which is green — sodium responds to green light but not to red. Converting 0.640 eV to joules gives 1.025 × 10−19 J, and with an electron mass of 9.109 × 10−31 kg the fastest electron leaves at about 474 km/s.
No Emission Is a Result, Not an Error
Shine red light on sodium and nothing comes off. Turn the lamp up until it is painfully bright and still nothing comes off. Wait an hour and nothing comes off. This is the observation that broke classical physics, and a calculator that returns a negative kinetic energy here is hiding the most important thing on the page.
Classical wave theory predicted the opposite in three ways. It said a brighter beam delivers energy faster, so emission should start at any frequency once enough energy has accumulated. It said the energy of emitted electrons should rise with intensity. And it said there should be a measurable delay at low intensity while the electron soaked up enough energy. None of it happens. Emission is instantaneous or absent, its threshold depends only on frequency, and intensity changes the number of electrons but never their energy.
Einstein's resolution was that light arrives in indivisible packets. An electron absorbs one whole photon or none. If that single packet carries less than the work function, the electron cannot escape, and doubling the number of packets simply means twice as many failures. Intensity is photons per second; frequency is joules per photon; only the second one can open the door.
When this tool reports no emission it still shows the threshold wavelength, so you can see exactly how far short the light falls and what source would work instead. That is the useful answer, and it is why this page exists alongside our simpler photon energy calculator, which returns the incident energy of a photon and stops there.
What Intensity Actually Changes
Brightness controls how many electrons are emitted per second, which is the saturation photocurrent. It has no effect whatsoever on the maximum kinetic energy, the stopping voltage or the threshold. Double the intensity above threshold and you get twice the current at exactly the same stopping voltage.
This is why the stopping voltage is the diagnostic measurement in a photoelectric experiment. Plot it against frequency for several sources on the same metal and you get a straight line whose gradient is the Planck constant divided by the elementary charge, and whose intercept on the energy axis is the work function. The gradient is the same for every metal, which is the strongest evidence that h is a property of nature rather than of the material.
One consequence catches people out. A very intense red laser will not eject a single electron from copper, while a feeble ultraviolet lamp will. Energy per photon is the only currency the surface accepts.
Where the Simple Model Stops Working
Four limits are worth stating. First, the equation gives a maximum, not a distribution: electrons originating below the surface lose energy on the way out, so most emerge with less, and the measured photocurrent falls off gradually as the retarding voltage rises rather than switching off sharply.
Second, the work function is a surface property and drifts. Oxidation, adsorbed gas and even the crystal face exposed can move it by several tenths of an electronvolt, which is why photocathodes are prepared and kept in vacuum.
Third, at very high intensities more than one photon can be absorbed effectively at once, and emission below the nominal threshold becomes possible. That is a femtosecond-laser regime, far from ordinary lamps, but it means the threshold is a statement about single-photon processes rather than an absolute prohibition.
Fourth, the speed shown here is non-relativistic. For kinetic energies approaching a few per cent of the electron rest energy of 511,000 eV, the classical expression starts to overstate the speed, and the tool flags that on the result. For those energies the relativistic kinetic energy calculator is the right tool, and the wave behaviour of the ejected electron belongs to the de Broglie wavelength calculator.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Expecting brighter light to eject faster electrons — intensity changes the number of electrons per second and nothing else. Only frequency sets their energy.
- Reading a negative kinetic energy as an answer — below threshold there is no emission at all. The correct output is a statement, not a negative number.
- Treating the work function as a fixed material constant — it belongs to the surface and shifts with oxidation, contamination and crystal face by several tenths of an electronvolt.
- Assuming every electron leaves with the maximum energy — the equation gives a ceiling. Electrons from below the surface arrive with less, producing a spread.
- Mixing joules and electronvolts mid-calculation — one electronvolt is 1.602 × 10−19 joules, and dropping that factor moves the answer by nineteen orders of magnitude.
Related Free Tools From Arb Digital
Get the energy of the incident photon on its own with the photon energy calculator, and move between wavelength, frequency and colour using the wavelength calculator or the frequency and period calculator. For the matter-wave behaviour of the electron once it is free, use the de Broglie wavelength calculator, and for energies where the classical speed formula breaks down, the relativistic kinetic energy calculator. Ordinary kinetic energy is handled by the kinetic energy calculator, atomic emission lines by the Rydberg equation calculator, and unit changes by the energy converter. Everything Arb Digital publishes is at the free online tools hub.
Frequently Asked Questions
Because an electron absorbs one whole photon, not a share of the beam. Intensity is the number of photons per second, so a brighter beam produces more emitted electrons but each one still receives exactly the same energy packet. Only frequency changes the energy per photon.
Nothing is emitted, at any intensity and for any duration. Each photon carries less than the work function, so no single absorption can free an electron, and more photons simply means more unsuccessful attempts. This calculator reports that as a result rather than returning a negative kinetic energy.
It is the retarding potential that just prevents the fastest emitted electron from reaching the collector, at which point the photocurrent falls to zero. Because kinetic energy equals the elementary charge times that voltage, the stopping voltage in volts is numerically the same as the maximum kinetic energy in electronvolts.
Measure the stopping voltage for several light frequencies on the same surface and plot voltage against frequency. The result is a straight line whose gradient is the Planck constant divided by the elementary charge. The intercept gives the work function of that surface, and the gradient is the same for every metal.
The work function is a property of the surface rather than the bulk metal, so it depends on which crystal face is exposed, on oxidation and on adsorbed gases. Differences of several tenths of an electronvolt between sources are normal. Use a measured value for your own sample where you have one.
No. The equation gives the ceiling, reached only by electrons that were already at the surface and lost nothing on the way out. Electrons freed deeper in the metal spend extra energy escaping, so the emitted population spreads from zero up to the maximum.
No, it uses the classical relationship between kinetic energy and speed. That is accurate while the kinetic energy is small compared with the electron rest energy of about 511,000 electronvolts, which covers ordinary ultraviolet sources comfortably. The tool warns you when the energy climbs far enough for the approximation to matter.
This tool is provided for educational and study use. It applies the single-photon photoelectric equation to an ideal clean surface and does not account for multiphoton absorption, surface contamination, thermal emission or the energy distribution of electrons originating below the surface.
