Calculation reviewed: 4 October 2026 · Engineering Desk Tools
How to use the Steam leak cost calculator
Estimate steam lost through a leak or vent, the heat and fuel it wastes, and the annual cost. Start with measurements or documented values for the equipment and reporting period you actually want to assess. The calculator does not fill in a typical installation for you. Its blank fields help keep a demonstration value from being mistaken for your own operating data.
Choose the required options, enter the values in the labelled units and select Calculate. If a field is rejected, check its range and unit before changing it. The result is accompanied by the equation and assumptions so you can decide whether it answers your engineering question.
Inputs and measurement basis
- Leak size input. Use hole mode when you can estimate the size of the opening. Use flow mode when you have a meter reading, a steam trap test result or a condensate measurement.
- Equivalent hole diameter (mm, hole mode). Equivalent round hole in mm. For a gland or flange weep, estimate the total open area and convert to a diameter. Ignored in flow mode. The allowed maximum is 100.
- Known steam flow (kg/h, flow mode). Measured or known steam loss in kg/h. Ignored in hole mode.
- Steam gauge pressure at the leak (bar g). Gauge pressure of the steam at the leak, in bar g (0 to 40). Use the line pressure upstream of the hole. The allowed maximum is 40.
- Discharge coefficient (0.72 is typical for a ragged leak). Accounts for the shape of the opening. 0.72 matches the DOE leak table for a rough re-entrant hole; a clean, rounded nozzle is nearer 0.95. Allowed range: 0.1 to 1.
- Boiler feedwater temperature (°C). Temperature of the water entering the boiler, including any condensate and economiser pre-heat, in °C. Allowed range: 5 to 125.
- Boiler efficiency on fuel (%). Boiler efficiency on the fuel you buy, in percent. Use your tested or reported figure. Typical gas-fired shell boilers are 80 to 90 percent. Allowed range: 30 to 99.
- Fuel cost per kWh of fuel energy (your currency). What a kWh of fuel energy costs you, in your own currency. For gas, divide the price per unit by kWh per unit.
- Hours the leak runs per year. Hours per year the leak is present and the boiler is firing to replace it. A leak on a steam main that is hot all year runs 8,000 hours or more. The allowed maximum is 8784.
Record the measurement source and operating condition. Retain unrounded values for verification.
Method and interpretation
A steam leak wastes the fuel that was burned to make the steam. The cost therefore has three parts: how much steam escapes, how much heat each kilogram carries, and what that heat costs at the boiler. The leak rate is either measured or estimated from the size of the hole. Steam escaping from a pressurised pipe, flange, valve gland or failed trap moves at sonic (choked) speed, so the flow depends on the hole area and the absolute upstream pressure. Doubling the hole diameter quadruples the loss, and each extra bar of pressure adds roughly the same proportion again.
Leak rate (kg/h) = 0.5252 × Cd × hole area (mm²) × absolute steam pressure (bar), the Napier relation for choked steam flow. Heat per kg = saturated steam enthalpy at the pressure − feedwater enthalpy. Fuel energy = heat ÷ boiler efficiency. Annual cost = fuel kWh × fuel price × hours.
Steam leaves a hole at choked (sonic) flow, so the rate depends on the hole area and the upstream absolute pressure and not on what it discharges to. The 0.5252 constant is the Napier equation W = 51.5 × A × P in imperial units, converted; with Cd 0.72 it reproduces the US Department of Energy leak table within about 2 percent. Enthalpies are saturated-steam values interpolated from IAPWS steam tables. Superheated steam, wet steam, flash steam from condensate and a steam trap passing live steam each differ somewhat. Use a measured flow where you have one. The cost is fuel only: add water, treatment and blowdown for the full cost of steam. Use one currency throughout.
Worked example
This example does not populate the form. Enter your own installation data.
Calculated result: 5,356.5869 annual cost. Steam enthalpy 2,768.4 kJ/kg at 7 bar g less feedwater 376.95 kJ/kg gives 2,391.45 kJ/kg. Fuel cost only, at the boiler efficiency you entered.
Check the arithmetic independently using the displayed equation. Retain intermediate precision and compare the final value with your equipment documentation.
Quick-reference table
These illustrative rows retain the worked example assumptions except for the varied input. They are not certified ratings or manufacturer data. Use the form for intermediate values.
Steam lost through a hole: quick reference
How the leak rate is calculated
The flow of steam out of a hole is choked, so for saturated steam it follows the Napier relation: W = 51.5 × A × P in lb/h, with A in square inches and P in psia. In metric units this is 0.5252 kg/h per mm² per bar absolute, multiplied by the discharge coefficient. The US Department of Energy leak table uses a coefficient of 0.72, and this calculator reproduces its figures within about 2 percent. For example, a 1/8 inch (3.175 mm) hole at 100 psig loses about 52 lb/h, or 23.7 kg/h.
Worked example
A 3 mm hole in a 7 bar g line leaks 21.42 kg/h. With 90 °C feedwater each kg carries about 2391 kJ, so the heat in the steam is 14.23 kW and, at 85 percent boiler efficiency, 16.74 kW of fuel. Over 8,000 hours at 0.04 per kWh that is 5,357 a year, from a hole only 3 mm across.
What this calculator leaves out
It prices the fuel only. Water treatment, make-up water, pumping and blowdown raise the true cost of a tonne of steam, and a leak that lets condensate escape also loses its heat. Where the leaking medium is a steam trap passing live steam, the loss is the same type of calculation, but the opening is partly blocked by condensate, so test with a thermographic gun or an ultrasonic tester before assuming a full-bore flow.
Common mistakes
Each kilogram of steam carries the difference between the enthalpy of saturated steam at line pressure and the enthalpy of the feedwater that replaces it, about 2,400 kJ (0.67 kWh) at 10 bar g with 90 °C feedwater. Dividing by boiler efficiency gives the fuel burned, and multiplying by the fuel price and the hours of leaking gives the cost. The result is fuel only. Treated water, pumping and blowdown add to the real cost of steam, and condensate that would otherwise be returned adds further heat that is lost with the leak. Before relying on the output, check the decimal format, unit scale and source of each value. Recheck unusual results against the formula.
Frequently asked questions
Are the example values used automatically?
No. Inputs remain blank when the tool opens or when you clear them. The worked example and table are reading material below the calculator. Enter the actual values you want to check each time, and label saved reports so their context is not lost.
What does the result mean?
The main result is the annual fuel cost of the leak. Steam lost is the mass leaving per hour, heat in the lost steam is the energy it carries above feedwater temperature, and fuel burned is that heat divided by boiler efficiency. Cost per tonne is the fuel-only cost of one tonne of steam at your conditions, a useful figure to compare against your steam cost from the energy report. Treat an estimate from hole size as an order of magnitude: a measured flow, or a leak of known size from the DOE table, is better.
Can I use a zero or a negative value?
The allowed range follows the meaning of each input. A divisor needs a positive value; other fields may allow zero. Check the form labels and error message rather than forcing an invalid value. A rejected input must be corrected before a result can be shown.
Is this a final design or equipment approval?
No. Steam leaves a hole at choked (sonic) flow, so the rate depends on the hole area and the upstream absolute pressure and not on what it discharges to. The 0.5252 constant is the Napier equation W = 51.5 × A × P in imperial units, converted; with Cd 0.72 it reproduces the US Department of Energy leak table within about 2 percent. Enthalpies are saturated-steam values interpolated from IAPWS steam tables. Superheated steam, wet steam, flash steam from condensate and a steam trap passing live steam each differ somewhat. Use a measured flow where you have one. The cost is fuel only: add water, treatment and blowdown for the full cost of steam. Use one currency throughout. Use the calculation as support for a checked decision, and review equipment documentation and applicable requirements before changing an installation or operating setting.
How can I save or share a calculation?
Calculate first, then use Copy result or Print report. Some maintenance tools also provide a CSV summary. Reports contain your own entered data, so review them before sharing. You can share the public page URL without including plant records or confidential measurements.
How do I report an unexpected result?
Use the Contact page and include the tool URL, input values, units, expected output and the reference you used. Explain the measurement basis. Exclude confidential information.
How do competitors calculate steam wastage?
Most steam leak calculators use the same three steps shown here: the leak flow from an orifice (Napier or choked-flow equation), the heat content above feedwater, and a fuel cost at boiler efficiency. The US Department of Energy steam tip sheet and most steam-system suppliers publish this method. Differences are mainly in the discharge coefficient and whether the steam cost per tonne is entered directly.
What is the cost of a steam leak per year?
Multiply the steam lost in kg/h by the hours of leaking, then by the cost of steam per kg. With the fuel-only method, the cost of one kg of steam is about 0.8 kWh of fuel at 10 bar g with 90 °C feedwater and 85 percent efficiency, which is 0.032 at 0.04 per kWh. The calculator does this for any pressure, feedwater temperature and fuel price.
Should I use steam cost per tonne instead of fuel cost?
If your plant reports a steam cost per tonne, multiply it by the tonnes lost for a more complete figure, because it includes water, treatment and electricity. The fuel-only value in this calculator is the minimum cost and is easy to defend because it needs only the boiler efficiency and fuel price.
Is steam venting from a feedwater tank the same calculation?
Yes, if you know the vent flow. Enter it in flow mode. If the vent is passing through a leaking bypass valve, estimate the opening area, or use the flow measured from condensate or steam meter readings before and after the repair.
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