Uranium Enrichment Calculator (SWU)

Compute separative work units needed to enrich uranium, or find product yield from an SWU budget.

Product Enrichment (xP)

wt% U-235

Tails Assay (xW)

wt% U-235

Feed Assay (xF)

wt% U-235

Product Mass (P)

kg U

SWU Budget

SWU

Product Enrichment (xP)

wt% U-235

Tails Assay (xW)

wt% U-235

Feed Assay (xF)

wt% U-235

SWU Required

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Natural Feed Required

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Tails Produced

—

Feed / Product Ratio

—

SWU / kg Product

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Product Yield

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Feed Required

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Tails Produced

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Feed / Product Ratio

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SWU / kg Product

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⚛️ What is the Uranium Enrichment SWU Calculator?

Separative work units (SWU) measure the effort required to separate uranium isotopes during the enrichment process. Natural uranium contains only 0.711% of the fissile isotope U-235, far too little for most reactor designs. Enrichment plants use centrifuge cascades to concentrate U-235 to the desired level, and SWU quantifies the isotopic separation work involved regardless of the technology used.

This calculator applies the standard mass balance and separation potential equations to compute three key outputs: the total SWU required, the mass of natural uranium feed consumed, and the mass of depleted uranium tails produced. A second mode works in reverse: given a fixed SWU budget, it computes the maximum quantity of enriched product that can be produced. Both modes are essential for uranium fuel cycle planning, reactor refueling analysis, and enrichment contract negotiation.

The value function V(x) = (2x-1)*ln(x/(1-x)) is the thermodynamic basis of the SWU formula. It was derived by Karl Cohen in the 1940s as part of the Manhattan Project and remains the universal standard for measuring isotopic separation work. The SWU formula is: SWU = P*V(xP) + W*V(xW) - F*V(xF), where P, W, and F are product, waste (tails), and feed masses, and xP, xW, xF are their respective U-235 assays. The mass balance requires F = P + W and F*xF = P*xP + W*xW.

Engineers and physicists use this calculator to optimize tails assay decisions, estimate feed requirements for fuel purchase contracts, and plan enrichment campaigns. A lower tails assay recovers more U-235 per ton of feed but consumes more SWU. A higher tails assay reduces SWU consumption at the cost of greater feed requirements. The optimal balance depends on the relative spot prices of natural uranium and enrichment services in the commercial market.

📐 Formula

SWU = P · V(x_P) + W · V(x_W) − F · V(x_F)

V(x) = (2x − 1) · ln[x / (1 − x)] — separation potential value function

P = product mass (kg U enriched to x_P)

W = tails (waste) mass (kg U at assay x_W)

F = feed mass (kg U at assay x_F); F = P + W

x_P = product enrichment (fraction); e.g. 0.04 for 4%

x_W = tails assay (fraction); typically 0.002 to 0.004

x_F = feed assay (fraction); natural U = 0.00711

Mass balance: F · x_F = P · x_P + W · x_W

Feed ratio: F/P = (x_P − x_W) / (x_F − x_W)

Tails ratio: W/P = (x_P − x_F) / (x_F − x_W)

Example: 1000 kg of 4% LEU from natural U with 0.3% tails requires 5,283 SWU and 9,002 kg of natural uranium feed.

📖 How to Use This Calculator

Steps

Enter product enrichment and tails assay - Type the desired U-235 enrichment percentage for the product (e.g. 4.0% for standard power reactor LEU) and the tails assay (e.g. 0.3%, the typical commercial value). Tails assay must be lower than feed assay.

Confirm feed assay - Enter the feed assay. Natural uranium is 0.711% U-235 by weight. If using depleted uranium from previous enrichment as feed, enter its actual assay, typically 0.2 to 0.4%.

Set product quantity - Enter the desired mass of enriched uranium product in kilograms. Click Calculate. The primary result shows SWU required, and secondary boxes show feed consumed, tails produced, and per-unit ratios.

Switch to Product from SWU mode for budget planning - Click the Product from SWU tab. Enter your available SWU budget and the same enrichment parameters. The calculator returns the maximum product mass you can produce with that SWU allocation.

💡 Example Calculations

Example 1 - Standard LEU for a Light-Water Power Reactor

Producing 25,000 kg of 4% LEU from natural uranium with 0.3% tails

Feed ratio F/P = (0.04 - 0.003) / (0.00711 - 0.003) = 0.037 / 0.00411 = 9.0024 kg feed per kg product.

Tails ratio W/P = F/P - 1 = 8.0024 kg tails per kg product. Feed required = 9.0024 x 25,000 = 225,061 kg. Tails = 8.0024 x 25,000 = 200,061 kg.

V(0.04) = 2.9238; V(0.003) = 5.7720; V(0.00711) = 4.8685. SWU/kg = 2.9238 + 8.0024 x 5.7720 - 9.0024 x 4.8685 = 5.283 SWU/kg.

Total SWU = 5.283 x 25,000 = 132,083 SWU

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Example 2 - Research Reactor LEU (19.75%)

Producing 100 kg of 19.75% LEU from natural uranium with 0.3% tails

Feed ratio F/P = (0.1975 - 0.003) / (0.00711 - 0.003) = 0.1945 / 0.00411 = 47.32 kg feed per kg product.

Feed required = 47.32 x 100 = 4,732 kg natural uranium. Tails = 46.32 x 100 = 4,632 kg.

V(0.1975) = (0.395-1)*ln(0.1975/0.8025) = -0.605 x (-1.401) = 0.8476. SWU/kg = 0.8476 + 46.32 x 5.7720 - 47.32 x 4.8685 = 37.75 SWU/kg.

Total SWU = 3,775 SWU from 4,732 kg of natural uranium

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Example 3 - Planning from a Fixed SWU Budget

How much 4.5% LEU can be produced from 50,000 SWU with 0.3% tails?

V(0.045) = (0.09-1)*ln(0.045/0.955) = -0.91 x (-3.055) = 2.780. SWU/kg = 2.780 + (W/P) x V(0.003) - (F/P) x V(0.00711).

F/P = (0.045 - 0.003)/(0.00711 - 0.003) = 0.042/0.00411 = 10.22. W/P = 9.22. SWU/kg = 2.780 + 9.22 x 5.7720 - 10.22 x 4.8685 = 5.754 SWU/kg product.

Product mass = 50,000 SWU / 5.754 SWU/kg = 8,690 kg. Feed required = 10.22 x 8,690 = 88,810 kg natural uranium.

Product yield = 8,690 kg of 4.5% LEU from 50,000 SWU

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❓ Frequently Asked Questions

What is a separative work unit (SWU) in uranium enrichment?+

A separative work unit (SWU) is the standard measure of the effort required to separate uranium isotopes during enrichment. It is defined by the equation SWU = P*V(xP) + W*V(xW) - F*V(xF), where V(x) = (2x-1)*ln(x/(1-x)) is the separation potential value function. SWU is not a unit of energy but of isotopic separation work. Larger SWU values indicate more isotopic separation was performed.

How much natural uranium feed is needed to produce 1 kg of 4% LEU?+

With natural uranium feed at 0.711% and a typical tails assay of 0.3%, producing 1 kg of 4% LEU requires approximately 9.0 kg of natural uranium and 5.28 SWU. The feed requirement drops to about 8.1 kg at 0.2% tails (but requires 6.8 SWU per kg), showing how tails assay optimization trades feed cost against enrichment service cost.

What is the separation potential value function V(x)?+

The value function V(x) = (2x-1)*ln(x/(1-x)) quantifies the isotopic content of a uranium stream at assay x. It is dimensionless and has a minimum at x = 0.5 (50% enrichment). For reference: V(0.00711) = 4.869 for natural uranium, V(0.003) = 5.772 for 0.3% tails, V(0.04) = 2.924 for 4% LEU. The SWU formula combines these to measure the net separation achieved.

What tails assay do commercial enrichment plants use?+

Commercial enrichment plants typically set tails assay between 0.2% and 0.35% U-235, depending on the relative cost of uranium feed versus SWU. When uranium is expensive relative to enrichment, plants choose a lower tails assay (0.2 to 0.25%) to extract more U-235 per tonne of feed. When enrichment is expensive, they raise the tails assay to save SWU at the expense of more feed consumption.

How do SWU and feed requirements trade off with each other?+

Lowering the tails assay reduces feed consumption but increases SWU consumption for the same product output, because more separation work is needed to extract U-235 down to a lower waste assay. Raising the tails assay reduces SWU consumption at the cost of greater feed requirements. Enrichers optimize this trade-off by comparing the spot market price of natural uranium (USD per kg U) against the enrichment service price (USD per SWU).

What enrichment level is defined as highly enriched uranium (HEU)?+

The IAEA defines highly enriched uranium (HEU) as uranium enriched to 20% U-235 or above. Weapons-grade HEU is enriched to 90% or more. Uranium below 20% is low-enriched uranium (LEU). Power reactor fuel uses LEU at 3 to 5%. Research reactors now use LEU at up to 19.75% under the RERTR program to eliminate HEU use in the civilian fuel cycle.

How many SWU does a 1000 MWe nuclear power plant require per year?+

A typical 1000 MWe light-water reactor requires roughly 100,000 to 120,000 SWU per year to produce its annual fuel reload of about 25 to 30 tonnes of enriched uranium. The global annual enrichment demand is roughly 50 to 60 million SWU, supplied mainly by Urenco (Europe), Orano (France), Rosatom (Russia), and CNEIC (China).

What is the difference between gaseous diffusion and centrifuge enrichment?+

Gaseous diffusion forces uranium hexafluoride (UF6) through porous membranes. The lighter U-235F6 diffuses slightly faster, providing a small separation factor per stage. It requires about 2,400 kWh per SWU. Gas centrifuge enrichment spins UF6 at high speed; centrifugal force concentrates heavier U-238F6 at the outer wall. It requires only about 50 kWh per SWU, making it about 50 times more energy efficient. All modern commercial plants use centrifuge technology.

How do I use this calculator for depleted uranium re-enrichment?+

Enter the actual assay of the depleted uranium in the feed assay field. For example, to re-enrich DU tails at 0.25% to produce 3% LEU with 0.1% new tails, enter xF = 0.25%, xP = 3%, xW = 0.1%. The mass balance and SWU formulas are identical to natural uranium feed. The feed-to-product ratio and SWU-to-product ratio will reflect the reduced separation needed starting from a richer feed.

What is reprocessed uranium (RepU) and can it be enriched?+

Reprocessed uranium (RepU) is the uranium separated from spent nuclear fuel after removing fission products and plutonium via the PUREX process. Spent LWR fuel typically contains 0.8 to 1.1% U-235 after discharge. RepU at this assay can be re-enriched to produce fresh LEU fuel, reducing natural uranium feed requirements. However, RepU contains U-232 and U-236 impurities that require additional shielding and handling precautions.

Why does the value function have a minimum at 50% enrichment?+

The value function V(x) = (2x-1)*ln(x/(1-x)) equals zero at x = 0.5 because separating a 50-50 mixture requires no net work by symmetry. Values above and below 50% are positive and increase as the mixture becomes more extreme (either very U-235-rich or very U-235-depleted). This mathematical property ensures that the SWU formula correctly measures the effort to move any uranium stream away from the 50-50 isotopic equilibrium toward either pure isotope.

What is the uranium hexafluoride (UF6) used in enrichment?+

Uranium hexafluoride (UF6) is the gaseous compound used as feed in modern uranium enrichment cascades. It is produced by chemically reacting uranium oxide (U3O8) with fluorine. UF6 has the advantage that fluorine is monoisotopic (only F-19 exists in nature), so all isotopic differences in the gas are due solely to U-235 and U-238. It sublimes at 56.5 degrees Celsius at atmospheric pressure, making it practical for gas centrifuge operations.

🔗 Related Calculators

What is a separative work unit (SWU) in uranium enrichment?

A separative work unit (SWU) is the measure of the effort required to separate uranium isotopes during enrichment. It is defined by the separative work function: SWU = P*V(xP) + W*V(xW) - F*V(xF), where V(x) = (2x-1)*ln(x/(1-x)) is the value function and P, W, F are product, waste, and feed masses. SWU is not a unit of energy but of isotopic separation work.

How much natural uranium is needed to produce 1 kg of 4% LEU?

With natural uranium feed (0.711% U-235) and a tails assay of 0.3%, producing 1 kg of 4% LEU requires about 9.0 kg of natural uranium feed and 5.3 SWU. The ratio changes significantly with tails assay: at 0.2% tails, about 8.1 kg feed and 6.8 SWU are needed per kilogram of product.

What is the value function V(x) in the SWU formula?

The value function V(x) = (2x-1)*ln(x/(1-x)) quantifies the isotopic content of a uranium stream at assay x. It is dimensionless and equals zero at 50% enrichment. For natural uranium (0.711%), V = 4.869. For 4% LEU, V = 2.924. For 0.3% tails, V = 5.772. The SWU formula combines these to measure the net separation achieved.

What is a typical tails assay for commercial enrichment?

Commercial enrichment plants typically operate between 0.2% and 0.35% tails assay. The optimal tails assay depends on the relative cost of natural uranium feed versus enrichment services. When uranium is expensive and SWU is cheap, enrichers set lower tails assay (0.2 to 0.25%) to extract more U-235 per kg of feed.

How is SWU related to uranium feed requirements?

SWU and feed requirements trade off against each other. Lowering the tails assay reduces feed consumption but increases SWU consumption, since more separation work is needed to push the waste stream to a lower assay. Raising the tails assay reduces SWU consumption at the expense of higher feed consumption. Enrichers optimize this trade-off based on spot market prices.

What enrichment level is considered highly enriched uranium (HEU)?

The IAEA defines highly enriched uranium (HEU) as uranium enriched to 20% U-235 or greater. Weapons-grade HEU is enriched to 90% or more. Uranium below 20% is classified as low-enriched uranium (LEU). Most power reactor fuel uses LEU at 3 to 5%. Research reactors now use LEU at up to 19.75% under the Reduced Enrichment for Research and Test Reactors (RERTR) program.

How many SWU does a nuclear power plant require per year?

A typical 1000 MWe light-water reactor requires roughly 100,000 to 120,000 SWU per year to supply its fuel. Annual fuel requirements are approximately 25 to 30 tonnes of enriched uranium at 3.5 to 4.5% enrichment. Global commercial enrichment capacity exceeds 60 million SWU per year, operated by Urenco, Orano, Rosatom, and others.

What is the difference between gaseous diffusion and centrifuge enrichment?

Gaseous diffusion separates UF6 gas through porous membranes exploiting the mass difference between U-235 and U-238. It is highly energy-intensive, consuming about 2,400 kWh per SWU. Gas centrifuge enrichment spins UF6 at high speed and uses far less energy, about 50 kWh per SWU, making it the dominant commercial technology. All major enrichment plants today use centrifuge technology.

How do I calculate the feed-to-product ratio for enrichment?

The feed-to-product ratio F/P = (xP - xW) / (xF - xW), where xP is product enrichment, xW is tails assay, and xF is feed assay (all as fractions). For 4% LEU from natural uranium with 0.3% tails: F/P = (0.04 - 0.003)/(0.00711 - 0.003) = 0.037/0.00411 = 9.00 kg feed per kg product.

Can this calculator be used for depleted uranium feed?

Yes. Enter the actual assay of the depleted uranium in the feed assay field. For example, if re-enriching depleted uranium tails at 0.2% assay to produce 3.5% LEU with 0.1% new tails, enter xF = 0.2%, xP = 3.5%, xW = 0.1%. The mass balance and SWU calculation remain identical to natural uranium feed.

What is the assay of spent nuclear fuel and can it be re-enriched?

Spent LWR fuel typically contains 0.8 to 1.1% U-235 after discharge, along with fission products and minor actinides. After reprocessing to remove fission products and plutonium (PUREX process), the residual uranium (RepU) at roughly 1% enrichment can be re-enriched. Re-enrichment of RepU saves natural uranium feed but requires additional handling precautions due to U-232 and U-236 contamination.

📌 Quick Tips

💡Natural uranium feed assay is 0.711% U-235 by weight. Depleted uranium (DU) from previous enrichment cascades has a lower assay, typically 0.2 to 0.4%.

💡Tails assay is a key economic variable. Lowering tails assay from 0.3% to 0.2% reduces feed consumption but increases SWU consumption for the same product.

💡Typical LEU for light-water power reactors requires 3 to 5% enrichment. Research reactors use 19.75% LEU (the non-HEU limit defined by the IAEA).

💡One kilogram of 4.5% LEU from natural uranium with 0.3% tails requires about 6.5 kg of natural uranium and roughly 5.5 SWU.

💡Global enrichment capacity is measured in millions of SWU per year (MSWU/yr). A 1000 MWe reactor requires about 100,000 to 120,000 SWU per year of fuel supply.