# Weighing the Neutrino

Laplace’s Mini World · Plate F61 · Energy, Flight & Sensing · Sensing

> When tritium decays, an electron and an antineutrino share a fixed energy. If the neutrino has mass, the fastest electrons fall just short of the end. KATRIN looks there.

- Interactive model: https://world.lapla.si/en/katrin/
- Embed: https://world.lapla.si/embed/en/katrin/
- 中文: https://world.lapla.si/zh/katrin/
- Updated: 2026-11-04

## 01 Below 0.45 eV

In April 2025 the KATRIN collaboration reported in Science that the neutrino’s mass is below 0.45 eV, at 90 % confidence. It is an upper limit, not a measured mass. The data come from the first five campaigns: 259 measurement days and about 36 million electrons.

The electron’s mass is 510,999 eV, more than a million times 0.45 eV (this page’s arithmetic). KATRIN’s first result, in 2019, was below 1.1 eV; in 2022 it was below 0.8 eV. The collaboration aims for better than 0.3 eV.

*below 0.45 eV (90 %) · 259 measurement days · about 36 million electrons · 2025*

## 02 Some mass, but how much

Neutrinos change type as they travel; this is called oscillation (see the plate “Neutrinos in Water and Ice”). Oscillation means they have mass. But it depends only on differences of squared masses: the Particle Data Group’s 2025 values are 7.50 × 10⁻⁵ and 2.451 × 10⁻³ eV². From these we know only that the heaviest is at least about 0.05 eV (the square root of the difference, this page’s arithmetic), not how heavy they are.

Cosmology gives tighter numbers: Planck’s 2018 data put the sum of the three masses below 0.12 eV, and DESI’s 2025 data below 0.064 eV in the standard cosmological model. These numbers depend on the model. KATRIN does not: it looks only at how the energy of one decay is shared.

*Δm²₂₁ = 7.50 × 10⁻⁵ eV² · Δm²₃₂ = 2.451 × 10⁻³ eV² · the heaviest at least about 0.05 eV*

## 03 Tritium decays

Tritium is a kind of hydrogen with one proton and two neutrons in its nucleus, and a half-life of 12.3 years. When it decays, a neutron becomes a proton and gives off an electron and an antineutrino. Each decay releases the same energy, about 18.6 keV, shared between the electron and the antineutrino. Any split is possible, so the electrons’ spectrum is a smooth curve.

The source is a stainless tube 10 m long and 90 mm across, cooled to 30 K, later 80 K. Tritium gas is fed in at the middle and spreads to both ends, which have no windows; about 40 g of tritium flows through it a day, giving up to 10¹¹ electrons a second. Superconducting magnets round it make 2.52 T, and the electrons run along the field lines towards both ends.

*T₂ → ³HeT⁺ + e⁻ + ν̄ₑ · half-life 12.3 years · about 18.6 keV · about 40 g of tritium a day*

## 04 The very end

The less the antineutrino takes, the closer the electron gets to the end of the spectrum. If the neutrino has mass, it always takes at least that mass’s energy, and the fastest electrons fall short of the end: the spectrum changes shape in its last few electronvolts. A mass of 0.45 eV changes only that last stretch.

Very few electrons land there: by the design report, only about 2 × 10⁻¹³ of the decays fall in the last 1 eV. So it takes a very strong source and a spectrometer that resolves electronvolts. The fit uses the data within 40 eV of the end.

*last 1 eV: about 2 × 10⁻¹³ of the decays · the fit uses the last 40 eV*

## 05 Only the fast get through

The main spectrometer’s tank sits at about −18.6 kV. Electrons arrive from ground potential and must climb this slope: those with more energy than the threshold get over and reach the detector; the rest stop in the middle of the tank and turn back. The spectrometer does not measure each electron’s energy; it counts how many are above the threshold.

A scan sets the threshold to up to 40 values, from 300 eV below the end to 135 eV above, for 17 s to several minutes each, about two to three hours a round. The fit uses only the points above 40 eV below the end; the points above the end see only background, about 0.1 to 0.3 counts a second.

*tank at about −18.6 kV · up to 40 thresholds a scan · background about 0.1⁠–⁠0.3 a second*

## 06 Set straight by the field

The potential slope holds back only the motion along the field. Electrons are born flying in every direction, circling the field lines. From 2.52 T in the source to 0.63 mT in the middle of the spectrometer the field falls by about four orders of magnitude; as it weakens slowly, almost all of the circling turns into forward motion, and the electrons are set straight.

What is not quite straightened sets the resolution: 18.6 keV times the ratio of 0.63 mT to 4.2 T, about 2.8 eV; with the design fields it is 0.93 eV. The pinch magnet, at 4.2 T, lets through only electrons emitted at less than about 51° to the field.

*2.52 T → 0.63 mT · ΔE ≈ 2.8 eV · emitted at less than about 51°*

## 07 Cut open: the tank

The main spectrometer is a tank of 316LN stainless steel: 23.23 m long, 9.8 m across inside, 1,240 m³, with walls 32 mm thick, weighing nearly 200 t. A cylinder in the middle, a cone at each end. Inside it is pumped to an ultra-high vacuum of about 10⁻¹¹ mbar.

Fifteen centimetres in from the wall run fine wires, mostly in two layers: 248 modules in 15 rings, at 160 to 200 V below the wall. Electrons knocked out of the wall by cosmic rays and radioactivity are pushed back by the wires and kept out of the middle. Here the tank is cut open at the front and top; the cut is painted red.

*23.23 × 9.8 m · 1,240 m³ · 10⁻¹¹ mbar · 248 wire modules*

## 08 The coils outside

Around the tank hang 14 air coils 12.6 m across: ordinary conductor, no iron. Together with the superconducting magnets along the line they shape the field in the tank, and can trim the field in the middle by up to 2 mT.

Two more sets of coils cancel the Earth’s field: in the middle of the tank the field is only 0.63 mT, so the Earth’s cannot be ignored. From the third campaign on, a new coil setting moved the analysing plane downstream and halved the background.

*14 coils, 12.6 m across · two sets against the Earth’s field · background halved*

## 09 Keeping the tritium back

The tritium gas has to stay on the source side: in the spectrometer its decays would be background. Between the two lies the transport section. The differential pumping section has 5 superconducting magnets, its tube turned by 20° from one piece to the next: the electrons follow the field lines round the bends, the gas molecules fly straight into the wall and are pumped away, cutting the flow by about five orders of magnitude.

Next comes the cryogenic pumping section: 7 magnets, a gold-plated tube cooled to 3 K and coated with frozen argon, which holds any tritium molecule that touches it, cutting the flow by at least seven more. The whole line cuts the tritium flow at least 10¹⁴-fold.

*differential pumping: about 10⁵ · cryogenic pumping: at least 10⁷ · whole line: at least 10¹⁴*

## 10 Counting electrons

Electrons that clear the threshold are gathered by the 4.2 T pinch magnet onto the detector: a single silicon wafer whose sensitive area, 90 mm across, is cut into 148 pixels of equal area, 4 in the middle and 12 rings of 12 around them.

Just before, the electrons are accelerated by about 10 kV more. The detector itself resolves only a few keV; its job is to count. The electronvolt resolution comes from the spectrometer’s threshold.

*148 pixels · sensitive area 90 mm across · about 10 kV more*

## 11 The long way round

The main spectrometer’s tank was welded in Deggendorf, in Bavaria. Karlsruhe is only 340 km away in a straight line, but the tank was too big for the roads and for the canal between the Danube and the Rhine. On 28 September 2006 it set off on a Danube freighter.

It went down the Danube to the Black Sea, by sea-going ship through the Bosporus, the Mediterranean, Gibraltar, the Atlantic and the North Sea, then up the Rhine: about 8,800 km. On 25 November it was landed at Leopoldshafen and covered the last 7 km by road, slowly through the village. Four days later it was lifted through the opened roof into its new hall.

*about 8,800 km · 28 September → 25 November 2006 · the last 7 km by road*

## 12 The result

What is recorded is the count above each threshold. In the fit, the endpoint energy, the source’s strength, the background and the squared neutrino mass m² are all left free. In 2025 the best fit was m² = −0.14 (+0.13/−0.15) eV²: below zero, and consistent with zero within the uncertainties. An m² below zero has no physical meaning.

From this comes the upper limit of 0.45 eV (90 % confidence). It says the neutrino is no heavier than that, not that its mass has been measured. On 26 October 2025 KATRIN completed its 1,000th measurement day, about five times the statistics of this result; that result is not yet published.

*m² = −0.14 (+0.13/−0.15) eV² · limit 0.45 eV · 1,000th measurement day: October 2025*

## 13 Taken apart

The air coils, the main spectrometer, the inner electrode, the pre-spectrometer, the transport section, the source and the detector rise one by one.

Point at a part (tap it on a phone) and it lifts on its own, with its name; the rest fade.

## 14 The laboratory

Two levers: the neutrino’s mass, and how far below the end the spectrometer’s threshold sits. The readouts give the counts a second above the threshold, and how many per cent fewer that is than with no mass; in the tank, electrons that clear it reach the detector, the others turn back.

This is this page’s toy model, not the collaboration’s analysis: the counts are scaled to the second campaign (3.68 million electrons, an electron-to-background ratio of 9.9, a background of 0.22 a second), only statistical scatter is counted, and the endpoint, strength, background and m² are all free. “Days to tell” is the scanning time for m² to stand 1.64 standard deviations from zero (90 %, one-sided).

**Try this**: In the lab, set the neutrino mass to 0.45 eV: 5 eV below the endpoint, how much lower is the count rate than with no mass, and how many days of data does it take to tell?

## What the model leaves out

The whole line is at 1:50. The published sizes are used as they are: the 70 m length, the main spectrometer’s 23.23 × 9.8 m, the 3.38 m pre-spectrometer, the source tube 10 m long and 90 mm across, the source cryostat’s 16 m, the cryogenic pumping section’s 7 m, the air coils’ 12.6 m. The rest is read off the paper’s drawings: the ribs outside the tank, the shape of its ends, the three pump ports, the outlines of the cryostats and magnets, the frames, and the source side’s floor standing higher than the spectrometer hall’s. The bends of the pumping sections are drawn as gentle zigzags. The wires in the tank are drawn as a see-through texture and the modules’ frames. The flux tube and the electrons’ spirals are schematic: the field lines come from this page’s simple coil model, the spirals are drawn many times too wide with far too few turns, and the electrons far too slow. The detector’s magnets are painted blue, as in photographs. The laboratory is a toy model, not the collaboration’s analysis.

## Common misconceptions

KATRIN gives an upper limit: below 0.45 eV, not a measured 0.45 eV. It measures electrons, not neutrinos; the spectrometer does not “catch” neutrinos. Oscillations show that neutrinos have mass but measure only differences of squared masses, not the masses themselves. 0.45 eV is an effective mass weighted by the mixing, not the mass of one kind of neutrino. A fitted m² below zero does not mean a negative squared mass; the best value fell below zero within its uncertainty. Cosmology’s limits are tighter, but they constrain the sum of the three masses and depend on the cosmological model. The tank is large not to hold more tritium but to let the field fall slowly and set the electrons straight. The detector cannot resolve electronvolts itself; that precision comes from the spectrometer’s threshold.

## Common questions

### How heavy is the neutrino?

In April 2025 the KATRIN collaboration reported in Science that the neutrino’s mass is below 0.45 eV, at 90 % confidence. It is an upper limit, not a measured mass.

See: [01 Below 0.45 eV](https://world.lapla.si/en/katrin/#limit)

### Why weigh the neutrino with tritium decay?

If the neutrino has mass, it always takes at least that mass’s energy, and the fastest electrons fall short of the end: the spectrum changes shape in its last few electronvolts.

See: [04 The very end](https://world.lapla.si/en/katrin/#endpoint)

### How does the KATRIN spectrometer pick out electrons?

The main spectrometer’s tank sits at about −18.6 kV. Electrons arrive from ground potential and must climb this slope: those with more energy than the threshold get over and reach the detector; the rest stop in the middle of the tank and turn back.

See: [05 Only the fast get through](https://world.lapla.si/en/katrin/#filter)

### How does the field set the electrons straight?

From 2.52 T in the source to 0.63 mT in the middle of the spectrometer the field falls by about four orders of magnitude; as it weakens slowly, almost all of the circling turns into forward motion, and the electrons are set straight.

See: [06 Set straight by the field](https://world.lapla.si/en/katrin/#collimate)

### How did the KATRIN main spectrometer get to Karlsruhe?

It went down the Danube to the Black Sea, by sea-going ship through the Bosporus, the Mediterranean, Gibraltar, the Atlantic and the North Sea, then up the Rhine: about 8,800 km.

See: [11 The long way round](https://world.lapla.si/en/katrin/#journey)

## Sources

1. [KATRIN Collaboration (2025): Direct neutrino-mass measurement based on 259 days of KATRIN data, Science 388, 180 (below 0.45 eV; m² = −0.14 (+0.13/−0.15) eV²; 36 million electrons; background; scans)](https://doi.org/10.1126/science.adq9592)
2. [KATRIN Collaboration (2022): Direct neutrino-mass measurement with sub-electronvolt sensitivity, Nature Physics 18, 160 (below 0.8 eV; 0.63 mT; 2.8 eV; KNM2 counts and background)](https://doi.org/10.1038/s41567-021-01463-1)
3. [KATRIN Collaboration (2019): An improved upper limit on the neutrino mass from a direct kinematic method by KATRIN, Phys. Rev. Lett. 123, 221802 (below 1.1 eV)](https://doi.org/10.1103/PhysRevLett.123.221802)
4. [KATRIN Collaboration (2021): The design, construction, and commissioning of the KATRIN experiment, JINST 16, T08015 (70 m; sizes and fields of the source, transport section, spectrometers, coils, inner electrode and detector; CC BY 4.0 drawings)](https://doi.org/10.1088/1748-0221/16/08/T08015)
5. [KATRIN Collaboration (2005): KATRIN Design Report 2004, FZKA 7090 (about 2 × 10⁻¹³ of the decays in the last 1 eV; about 200 t)](https://www.katrin.kit.edu/publikationen/DesignReport2004-12Jan2005.pdf)
6. [Karlsruhe Institute of Technology (2025): Neutrinos weigh less than 0.45 electronvolts, press release 029/2025](https://www.kit.edu/kit/english/pi_2025_029_astroparticle-physics-neutrinos-weigh-less-than-0-45-electronvolts.php)
7. [Max Planck Institute for Nuclear Physics (2025): 1000 days of neutrino mass measurements (26 October 2025)](https://www.mpi-hd.mpg.de/mpi/en/public-relations/news/news-item/1000-days-of-neutrino-mass-measurements)
8. [Gumbsheimer et al. (2007): Elektrostatische Spektrometer und Detektoren für KATRIN, Nachrichten – Forschungszentrum Karlsruhe 39, 75 (−18.6 kV; Deggendorf; 340 km; 25 November; the last 7 km; into the hall four days later)](https://publikationen.bibliothek.kit.edu/120067967/3814979)
9. [Forschungszentrum Karlsruhe (2006): Ein Koloss auf großer Fahrt, Research to Business 4|2006 (8,800 km; 28 September; the route)](https://publikationen.bibliothek.kit.edu/1000041975/3150285)
10. [Physics Today (2007): Detector on the move, 60(2), 100 (neither the roads nor the Danube–Rhine canal)](https://doi.org/10.1063/1.2711653)
11. [Particle Data Group (2025): Neutrino Masses, Mixing, and Oscillations (oscillations depend only on the differences of squared masses; the heavier at least √Δm²)](https://pdg.lbl.gov/2025/reviews/rpp2025-rev-neutrino-mixing.pdf)
12. [Particle Data Group (2025): Lepton Summary Table (Δm²₂₁ = 7.50 × 10⁻⁵ eV², Δm²₃₂ = 2.451 × 10⁻³ eV²)](https://pdg.lbl.gov/2025/tables/rpp2025-sum-leptons.pdf)
13. [Planck Collaboration (2020): Planck 2018 results. VI. Cosmological parameters, A&A 641, A6 (Σm \< 0.12 eV)](https://doi.org/10.1051/0004-6361/201833910)
14. [DESI Collaboration (2025): DESI DR2 Results II, arXiv:2503.14738 (Σm \< 0.064 eV in ΛCDM)](https://arxiv.org/abs/2503.14738)
15. [CODATA 2022: electron mass energy equivalent (0.510 998 950 69 MeV)](https://physics.nist.gov/cgi-bin/cuu/Value?mec2mev)

## Data

The beamline follows the KATRIN collaboration’s drawings in Aker et al., JINST 16, T08015 (2021) (CC BY 4.0): the layout (Fig. 2), the air-coil system (Fig. 41), the main spectrometer’s vacuum scheme and the wire electrode. The published sizes are used where they exist (the 70 m line, the main spectrometer’s 23.23 m × 9.8 m, the 12.6 m air coils, the 10 m × 90 mm source tube, the 3.38 m pre-spectrometer); the rest is read off the drawings, and the notes list what is simplified. The spectrum, the share of decays near its end, the energy resolution, the field and flux-tube drawing and the laboratory’s toy are computed by this page (docs/plates/katrin/computed-\*.py, tests/katrin.test.js); the toy is not the collaboration’s analysis. Material presets, parts and the softbox studio of the site’s model kit are ported from AirsupHQ/machine-skill (MIT, © 2026 Air Supply Technologies Inc.).

## Licence CC BY-NC 4.0

The text, pictures and models on this page are licensed CC BY-NC 4.0: free to use and adapt for teaching and other non-commercial purposes, with credit to world.lapla.si. Third-party material listed above keeps its own licence.

https://creativecommons.org/licenses/by-nc/4.0/deed.en

## Cite this plate

Laplace’s Mini World, Plate F61, “Weighing the Neutrino”, https://world.lapla.si/en/katrin/, CC BY-NC 4.0, updated 2026-11-04.