Key facts
- Uranium makes up about 84.8% of the mass of U3O8 and about 67.6% of UF6, from atomic masses.
- One tonne of 4.5% product at 0.25% tails needs about 9.2 t U of feed, equivalent to about 10.9 t U3O8 or 13.6 t UF6.
- Mass of U-235 is conserved across enrichment: feed U-235 equals product plus tails U-235.
- Real plants add losses and process holdup that the idealised balance omits.
Why a material balance is the starting point
Every step in the front end of the fuel cycle changes either the chemical form or the isotopic composition of uranium, and quantities are quoted in different units at different stages: pounds or tonnes of U3O8 for mine output and market trading, kilograms of uranium in UF6 for conversion and enrichment, and kilograms of heavy metal for fuel fabrication. A material balance ties these together. Two principles do most of the work: uranium mass is conserved across enrichment, and so is the mass of U-235. Everything else is chemistry, in the form of fixed mass ratios.
The overview of how the stages fit together is on the fuel production chain page; the separative-work side of enrichment is covered by the SWU calculator.
Conversion factors between U, U3O8 and UF6
The factors follow from atomic masses of uranium (about 238.03), oxygen (about 16.00) and fluorine (about 19.00). U3O8 has a molar mass of about 842.1, of which three uranium atoms account for 714.1, so uranium is about 84.8% of the mass. UF6 has a molar mass of about 352.0, of which uranium is 238.03, about 67.6%.
| Form | Uranium fraction by mass | Mass per 1 kg U |
|---|---|---|
| U | 100% | 1.000 kg |
| U3O8 | 84.8% | 1.179 kg |
| UF6 | 67.6% | 1.479 kg |
Commercial concentrate is not pure U3O8; the World Nuclear Association describes it as typically containing more than 80% uranium by mass. The calculator uses the stoichiometric 84.8% figure, so a real shipment's assay should be used where it is known. Trade in the oxide is conventionally quoted in pounds, with 1 lb equal to 0.45359237 kg.
The enrichment balance equations
With product mass P, feed mass F and tails mass T (all in kg U), and U-235 mass fractions xp, xf and xt:
- Total uranium: F = P + T
- U-235: F · xf = P · xp + T · xt
Solving gives F = P · (xp − xt) / (xf − xt) and T = F − P. The ratio F/P rises steeply as the tails assay rises towards the feed assay. Defaults in the calculator are 1,000 kg U of product at 4.5%, tails at 0.25% and feed at 0.711%.
Worked example: one tonne of 4.5% product
For 1,000 kg U of product at 4.5% with 0.25% tails and 0.711% feed:
- Feed: 1,000 × (0.045 − 0.0025) / (0.00711 − 0.0025) ≈ 9,219 kg U.
- Tails: 9,219 − 1,000 ≈ 8,219 kg U.
- U-235 check: feed 9,219 × 0.00711 ≈ 65.5 kg; product 45.0 kg plus tails about 20.5 kg.
- Feed as U3O8: 9,219 / 0.848 ≈ 10,870 kg, which is about 23,970 lb.
- Feed as UF6: 9,219 / 0.676 ≈ 13,640 kg.
- Product as UF6: 1,000 / 0.676 ≈ 1,479 kg.
In other words, about 11 tonnes of oxide concentrate stand behind one tonne of enriched uranium at these settings, and roughly 89% of the feed uranium leaves as depleted tails. That depleted uranium is itself a stock with uses and liabilities, discussed on the depleted uranium page.
The same method applies to a reactor-scale batch. The World Nuclear Association gives, for a 1,000 MWe reactor, about 24.3 t of enriched uranium per year at 4.5% with a 0.22% tails assay, using 211 t of natural uranium (249 t U3O8). Applying the formula above gives 24.3 × (0.045 − 0.0022) / (0.00711 − 0.0022) ≈ 212 t U, consistent with that figure.
How the tails assay moves the balance
For 1,000 kg of 4.5% product and 0.711% feed, calculated from the equations above:
| Tails assay | Feed (kg U) | Feed as U3O8 (kg) | Tails (kg U) |
|---|---|---|---|
| 0.20% | 8,415 | 9,924 | 7,415 |
| 0.25% | 9,219 | 10,872 | 8,219 |
| 0.30% | 10,219 | 12,051 | 9,219 |
A tails assay of 0.30% instead of 0.20% adds about 21% to the feed requirement. The separative work moves the opposite way; the full trade-off is tabulated on the SWU calculator page.
Assumptions and what the calculator leaves out
The balance is idealised. It assumes complete conversion and no losses at any step, a two-isotope uranium mixture, and a single steady state in which feed, product and tails assays are fixed. In practice, small percentages of uranium are lost or held up in conversion, enrichment and fabrication, and recycled or off-specification material can alter the isotopic mix. Results should therefore be treated as lower-bound requirements for planning exercises, not as contractual quantities. Cost conversion needs prices, which the calculator does not use; the cost structure is outlined on the fuel-cost page.
Frequently asked questions
How much U3O8 is needed for one kilogram of enriched uranium?
At 4.5% product and 0.25% tails, about 10.9 kg of U3O8 (about 9.2 kg of uranium) per kilogram of enriched uranium, using the 84.8% uranium fraction of U3O8.
Why is uranium only 67.6% of UF6 by mass?
Each uranium atom (about 238 u) is bonded to six fluorine atoms (about 19 u each), so fluorine accounts for roughly a third of the compound's mass.
Are the calculator's results the same as real plant quantities?
No. They are idealised and exclude process losses, holdup and the actual assay of concentrate, so real requirements are somewhat higher.
What happens to the tails?
The tails, known as depleted uranium, are stored, usually as UF6 or in converted oxide form, and may be re-enriched or used in other applications.
How many pounds of U3O8 is one tonne of U3O8?
One metric tonne is about 2,204.6 lb, from 1 lb = 0.45359237 kg.
Sources and further reading
- World Nuclear Association — Uranium Enrichment (2024)
- World Nuclear Association — Nuclear Fuel Cycle Overview (2024)
- World Nuclear Association — Conversion and Deconversion (2024)
- World Nuclear Association — Fuel Fabrication (2024)
- World Nuclear Association — Economics of Nuclear Power (2024)
- US Energy Information Administration — Uranium Marketing Annual Report (2024)
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