Neutrinovoltaics · Holger Thorsten Schubart

The Schubart Master Formula

The first consolidated equation for converting the invisible spectrum of ambient radiation into usable electrical power — published by Holger Thorsten Schubart of the Neutrino® Energy Group, and explained here parameter by parameter.

P \;=\; \int \Phi(E,\theta)\,\sigma(E)\,\Delta p\,v_{\text{ph}}\,\eta_{\text{conv}}\;dE\,d\theta

Power = integral over energy E and angle θ of radiation flux density × cross-section × momentum transfer × phonon velocity × conversion efficiency

Understand the formula → Explore the deep dives

Canonical publication · the symbol P(t) →

equation uniting five physical parameters

10¹⁴

solar neutrinos through each cm² every second

2024

year the Master Formula was published

24/7

ambient flux — day, night, indoors, underground

Nobel Prize 2015Neutrino mass established

Patent WO2016142056A1Core conversion architecture

34,000+ citationsUnderlying peer-reviewed research

Since 200818 years of R&D

Where to begin

Whether you want the plain-language idea, the exact mathematics, or the peer-reviewed physics it rests on, there is a path for you.

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The Master Formula

The exact equation of neutrinovoltaics, read symbol by symbol and put in the foreground.

P = \int \Phi(E,\theta)\,\sigma(E)\,\Delta p\,v_{\text{ph}}\,\eta_{\text{conv}}\;dE\,d\theta

Understand the formula →

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What is neutrinovoltaics?

A plain-language introduction to harvesting energy from the invisible radiation spectrum.

Read the overview →

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The research behind it

Peer-reviewed papers underpinning each parameter of the formula.

Browse research →

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Run the numbers

An interactive calculator built on the five parameters of the formula.

Open the calculator →

Grounded in a century of physics from institutions worldwide

Max Planck SocietyFraunhoferHelmholtzCERNETH ZürichImperial College LondonCambridgeOxfordUniversity of TokyoMITStanfordFermilabBrookhavenNRELMax Planck SocietyFraunhoferHelmholtzCERNETH ZürichImperial College LondonCambridgeOxfordUniversity of TokyoMITStanfordFermilabBrookhavenNREL

The core idea: the invisible radiation reaching Earth — cosmic and terrestrial, neutrinos included — is enormous and essentially constant. Inside a multilayer graphene–silicon material, that flux and the thermal motion of the atoms are rectified into a directed current. The Master Formula is the exact bookkeeping of how much power results.

The five parameters at a glance

Each factor in the formula is a link in a chain. The radiation flux density sets how much invisible radiation arrives; the scattering cross-section sets how strongly it couples to the material; the momentum transfer is the push each interaction delivers; the phonon velocity sets how fast the lattice carries it; and the conversion efficiency is the fraction that becomes usable power output.

“The universe has always provided energy in abundance. Our task is not to create it, but to learn the language in which it is offered — and to build the architecture that can receive it.”

Holger Thorsten SchubartCEO & Mathematician, Neutrino Energy Group

Scientific context. The Master Formula rests on established, Nobel-recognised physics — neutrino oscillation, coherent elastic neutrino–nucleus scattering, and the electronic properties of graphene. As the Neutrino Energy Group itself frames it, the work ahead is to separate what is already experimentally established from what still requires independent validation at full scale. This site presents the formula and its foundation as published by Holger Thorsten Schubart.

How neutrino energy works → See the derivation