Key facts
- One kilogram of 4.5% U-235 product needs about 9.2 kg of natural-uranium feed and about 6.9 SWU at a 0.25% tails assay (ideal-cascade formula).
- Raising the tails assay saves SWU but costs feed uranium; lowering it does the opposite.
- Centrifuge plants use roughly 40-50 kWh per SWU, gaseous diffusion plants roughly 2,400-2,500 kWh per SWU (World Nuclear Association).
- SWU is a measure of work done, not of mass: it depends on the assays at all three streams.
What a separative work unit actually measures
Natural uranium contains about 0.711% U-235 by atom fraction. Reactor fuel for light-water reactors is typically enriched to a few percent, and the separation is done by moving the isotope ratio of uranium hexafluoride gas stage by stage in a cascade. The effort needed depends not on how much material is processed in total but on how far the product is pushed above the feed assay and how far the tails are depleted below it. The separative work unit (SWU) is the standard measure of that effort. It is expressed in kilogram SWU for commercial contracts, and plant capacities are normally quoted in thousands of SWU per year.
Because SWU is a measure of work rather than of energy, one SWU is not a fixed number of kilowatt-hours. The World Nuclear Association notes that modern gas-centrifuge plants need on the order of 40-50 kWh per SWU, whereas the older gaseous-diffusion plants needed some 2,400-2,500 kWh per SWU. The energy implications of that difference are discussed on the fuel-cycle energy balance page.
The three equations behind the calculator
The calculator uses the textbook ideal-cascade relations. Let P be the product mass (kg U), F the feed mass and T the tails mass, with U-235 mass fractions xp, xf and xt respectively.
- Feed: F = P · (xp − xt) / (xf − xt)
- Tails: T = F − P
- Value function: V(x) = (1 − 2x) · ln((1 − x) / x)
- Separative work: SWU = P · V(xp) + T · V(xt) − F · V(xf)
The first two lines are simply conservation of uranium and of U-235. The third line defines the value function, a mathematical device that lets the work of a cascade be written as a sum over the three streams. The units of SWU come out the same as the units of the masses: kg SWU if the masses are in kilograms of uranium.
The defaults in the calculator are P = 1,000 kg U, product assay 4.5%, tails assay 0.25% and feed assay 0.711%. Feed mass is quoted as kilograms of uranium, not of the chemical compound; conversion to U3O8 or UF6 is handled on the material balance calculator.
Worked example: one tonne of 4.5% product
Using the default inputs, the calculation proceeds as follows.
- Feed: F = 1,000 × (0.045 − 0.0025) / (0.00711 − 0.0025) ≈ 9,219 kg U, a feed-to-product ratio of about 9.22.
- Tails: T = 9,219 − 1,000 ≈ 8,219 kg U.
- Value function values: V(0.045) ≈ 2.780, V(0.0025) ≈ 5.959, V(0.00711) ≈ 4.869.
- Separative work: SWU = 1,000 × 2.780 + 8,219 × 5.959 − 9,219 × 4.869 ≈ 6,871 SWU, or about 6.87 SWU per kilogram of product.
As a check on the arithmetic, U-235 in equals U-235 out: 9,219 kg × 0.711% ≈ 65.5 kg in the feed, against 45.0 kg in the product plus 20.5 kg in the tails.
The same formulas reproduce a figure published by the World Nuclear Association: about 7.9 SWU per kilogram of 5% product at a 0.25% tails assay, and about 8.9 SWU at a 0.20% tails assay. Calculated with the equations above, one kilogram of 5% product gives roughly 7.92 SWU at 0.25% and 8.85 SWU at 0.20%.
The tails-assay trade-off
Enrichers and buyers can choose the tails assay, and the choice shifts cost between two inputs: natural uranium and separative work. The table shows the effect for 1,000 kg of 4.5% product with a 0.711% feed, calculated from the formulas above.
| Tails assay | Feed (kg U) | Separative work (SWU) |
|---|---|---|
| 0.20% | 8,415 | 7,690 |
| 0.25% | 9,219 | 6,871 |
| 0.30% | 10,219 | 6,231 |
| 0.35% | 11,496 | 5,710 |
A lower tails assay saves feed but needs more SWU; a higher one does the reverse. Which setting is cheapest depends on the relative prices of uranium and enrichment, which change over time, so no single tails assay is universally optimal. The World Nuclear Association reports that Western plants are typically designed for tails of about 0.18-0.22% U-235 and Russian cascades for about 0.10%, and that the choice of operating tails can be adjusted within the limits of installed capacity. Underfeeding, that is running a plant at a lower tails assay using less feed, and overfeeding are the terms used for that operational flexibility.
Using the calculator
Set the product mass in kilograms of uranium, then the three assays as percentages of U-235 by mass. The calculator returns feed, tails and SWU. Typical inputs for light-water reactor fuel fall between about 3% and 5% product; the 5% figure is also the usual licensing limit of fabrication plants for criticality-safety reasons (World Nuclear Association). Natural-uranium feed is 0.711%; entering a different feed assay, such as reprocessed or previously depleted material, is allowed, but the result is only as good as the assay entered.
Scaling is linear in product mass: doubling P doubles F, T and SWU. This makes the calculator convenient for annual reload estimates. A typical 1,000 MWe light-water reactor uses roughly 24 tonnes of enriched uranium per year at 4.5% (World Nuclear Association), which, at the 0.25% tails of the example above, would mean about 24 times the figures calculated for one tonne.
Limits of the ideal-cascade method
The formulas describe a theoretical ideal cascade, in which no work is wasted on mixing streams of different composition. Real plants differ in several ways. Cascades have finite numbers of machines and stages, and their performance depends on machine type, so the SWU a plant actually delivers per unit of installed capacity will deviate from the ideal. The calculation also assumes that only the two isotopes U-235 and U-238 matter; minor isotopes such as U-234 and U-236, present in recycled feed, change cascade behaviour and are ignored.
The result does not include the quantities that surround the enrichment step: conversion losses, yield losses in fabrication, or the price of anything. For those, see the fuel-cost page. For the processes before and after enrichment, see the fuel production chain. The page describes generic principles and is not a substitute for a supplier's contractual SWU accounting, which may use specific conventions and loss allowances.
Frequently asked questions
What is a SWU?
A separative work unit is the standard measure of the effort required to separate uranium isotopes. It depends on the product, tails and feed assays and on the quantities of each stream, and is quoted in kg SWU.
How much SWU does one kilogram of 4.5% enriched uranium need?
With a 0.711% feed and a 0.25% tails assay, the ideal-cascade formula gives about 6.87 SWU per kilogram of product, using about 9.2 kg of natural-uranium feed.
Why does a higher tails assay reduce the SWU needed?
Less U-235 is stripped from the waste stream, so the plant does less separation. The price is that more feed uranium is needed to obtain the same amount of product.
Is SWU the same as kilowatt-hours?
No. SWU measures separative work, whereas energy consumption per SWU depends on the technology. The World Nuclear Association gives roughly 40-50 kWh per SWU for centrifuges and about 2,400-2,500 kWh per SWU for gaseous diffusion.
Does the calculator account for U-236 or other minor isotopes?
No. It treats uranium as a two-isotope mixture of U-235 and U-238, so results for recycled feed are approximate.
Sources and further reading
- World Nuclear Association — Uranium Enrichment (2024)
- World Nuclear Association — Nuclear Fuel Cycle Overview (2024)
- World Nuclear Association — Fuel Fabrication (2024)
- World Nuclear Association — Economics of Nuclear Power (2024)
- US Energy Information Administration — Uranium Marketing Annual Report (2024)
- World Nuclear Association — Conversion and Deconversion (2024)
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