A capillary tube is the simplest expansion device in refrigeration: a long, narrow, fixed-bore length of drawn copper that drops liquid refrigerant from condensing pressure to evaporating pressure purely by friction and flashing. There is no valve, no bulb, no diaphragm and no adjustment. The calculator above gives a first-pass length for such a tube from the duty you need, the pressure difference you have to absorb, and the refrigerant properties you enter yourself.
Arb Digital builds free engineering calculators that state their own limits honestly rather than presenting a rough model as a finished design. This one is deliberately built around a single-phase liquid friction model, and the sections below explain exactly where that model stops being true. Treat the number as a starting length for a bench trial, not as a part specification.
What This Capillary Tube Sizing Calculator Does
The tool works in four steps. It converts your cooling duty into a refrigerant mass flow using the refrigerating effect you supply. It converts that mass flow into a mean liquid velocity through the bore you specify. It works out the Reynolds number and the corresponding Darcy friction factor. Then it asks how many metres of that tube it would take to consume the pressure difference between the condenser and the evaporator, using the Darcy–Weisbach relation.
Every refrigerant property is a user input. There is no refrigerant table on this page, and that is deliberate. Density, viscosity and refrigerating effect all change with the saturation temperatures you are working between, and a table of single values for R134a or R600a would be wrong for most of the conditions a reader might type in. The right source is a published thermophysical property database queried at your own condensing and evaporating conditions.
The grid gives the four intermediate numbers that tell you whether the answer is sensible: mass flow, mean velocity, Reynolds number and pressure gradient. If any looks absurd, the length is absurd too, and the input that caused it is usually the bore.
How to Use It
- Start from the duty, not the compressor. Enter the heat the evaporator has to absorb in watts. A compressor rating is a different number and includes losses this calculation does not model.
- Read the refrigerating effect off your own cycle. It is the enthalpy rise across the evaporator between the state leaving the capillary tube and the state entering the compressor, at your pressures and your superheat.
- Enter absolute pressures. Gauge pressure will understate the pressure difference by about one bar at each end and will give you a tube that is far too short.
- Change the bore before you change anything else. Required length is extraordinarily sensitive to diameter. A ten per cent change in bore moves the length by roughly half.
- Read the Reynolds number. Below about 2,300 the flow is laminar and the tool uses the exact laminar friction law. Above about 4,000 it uses the smooth-tube turbulent correlation. In between, treat the answer as indicative only.
The Formula: How the Length Is Calculated
Mass flow comes straight from the energy balance: ṁ = Q ÷ Δh, where Q is the duty in watts and Δh is the refrigerating effect in joules per kilogram. Mean velocity follows from continuity, V = ṁ ÷ (ρA), with A the bore area πD² ÷ 4.
The Reynolds number is Re = ρVD ÷ μ. For laminar flow the Darcy friction factor is exactly f = 64 ÷ Re. For turbulent flow in a smooth tube the tool uses the Blasius correlation f = 0.3164 × Re−0.25, and where you enter a non-zero relative roughness it solves the Colebrook–White relation iteratively instead. The same friction machinery sits behind the friction factor calculator and the pipe flow calculator, and the Reynolds number calculator handles the flow-regime question on its own.
Length then comes from Darcy–Weisbach rearranged for L: ΔP = f × (L ÷ D) × (ρV² ÷ 2), so L = 2DΔP ÷ (fρV²). Reference values for refrigerant density, viscosity and enthalpy at your own conditions should come from the NIST Chemistry WebBook thermophysical properties of fluid systems, which is the defensible source for every property input on this page.
Work the defaults by hand. A 1,000 W duty with a 150 kJ/kg refrigerating effect gives ṁ = 1,000 ÷ 150,000 = 0.006667 kg/s. A 0.8 mm bore has an area of 5.027 × 10−7 m², so at 1,200 kg/m³ the velocity is 0.006667 ÷ (1,200 × 5.027 × 10−7) = 11.05 m/s. Then Re = 1,200 × 11.05 × 0.0008 ÷ 0.00018 = 58,900, which is firmly turbulent, and Blasius gives f = 0.3164 ÷ 58,9000.25 = 0.0203. With ΔP = 14 bar = 1.4 × 106 Pa, L = 2 × 0.0008 × 1,400,000 ÷ (0.0203 × 1,200 × 11.05²) = 2,240 ÷ 2,977 = 0.75 m.
Why the Real Tube Is Longer Than This Number
The model above treats the refrigerant as a liquid all the way along the tube. It is not. Somewhere partway down, the local pressure falls below the saturation pressure at the local temperature and the refrigerant begins to flash. From that point the fluid is a two-phase mixture whose density collapses, whose velocity climbs steeply, and whose frictional pressure gradient rises by an order of magnitude. The flashing region does most of the pressure-dropping work in a real capillary tube, and it does it in far less length than the single-phase model predicts.
There is a second complication. Refrigerant in a smooth capillary tube frequently does not flash at the equilibrium saturation point at all. It goes metastable, staying liquid below its saturation pressure until a nucleation site or a disturbance triggers vaporisation, sometimes several centimetres further along than theory says. That delay is real, it is repeatable, and it is one reason two nominally identical tubes can behave measurably differently.
Finally, a capillary tube can choke. Once the two-phase flow reaches the local sonic velocity at the outlet, lowering the evaporating pressure further does not increase the mass flow at all. A choked capillary tube is insensitive to the evaporator, which changes the whole character of the system. None of this is in the arithmetic above, which is precisely why the output is an indicative starting length and not a design.
What Actually Sets the Length in Practice
The honest answer is that charge, subcooling and system balance set it. A capillary system has no receiver and no reserve, so the refrigerant charge is a design variable in its own right. Overcharge it and liquid backs up into the condenser, raising head pressure and pushing more flow through the tube. Undercharge it and vapour enters the capillary tube inlet, which cuts mass flow dramatically because vapour is far less dense than liquid.
Subcooling at the tube inlet matters for the same reason. A few degrees of subcooling guarantees solid liquid at the entrance and pushes the flash point further along, both of which increase mass flow for the same tube. That is why capillary systems are commonly built with a suction-line heat exchanger: the cold suction gas subcools the liquid feeding the tube, and the tube is then sized around that state rather than around saturated liquid.
Everything then has to balance. The compressor, the condenser, the capillary tube and the evaporator each have their own pressure-flow characteristic, and the system settles at the single operating point where all four agree. Sizing the tube is really the act of choosing where that balance point lands. Getting it right is done on a test rig with a variable-length coil and instrumentation, by trimming, measuring and re-trimming.
How This Sits Next to a Thermostatic Expansion Valve
A capillary tube is chosen for cost, simplicity and reliability, and accepted for its lack of control. Because it is a fixed restriction, it delivers the right flow at exactly one condition and something other than the right flow at every other condition. At low ambient the head pressure falls, flow falls, and the evaporator starves. At high ambient the head pressure rises and the evaporator can flood back toward the compressor.
A thermostatic or electronic expansion valve modulates to hold superheat, so it tracks load and ambient. It also costs more, has moving parts, and needs its own sizing and setting. That is the trade: capillary tubes dominate small hermetic systems such as domestic refrigerators, dehumidifiers and small packaged units, where the operating range is narrow and the price of a valve is a large fraction of the price of the machine.
Where This Sits Among the Other Flow Tools
This page owns one narrow job: the fixed-restriction expansion device in a refrigeration circuit. For general duct and pipe pressure loss, use the pipe flow calculator. For a sharp-edged restriction rather than a long one, the orifice flow calculator is the right model, because an orifice loses pressure to a sudden contraction rather than to wall friction along a length. For the energy side of the cycle, the enthalpy calculator and the latent heat calculator handle the state changes, and the AC BTU calculator works the room-load question that decides your duty in the first place. The viscosity converter and the mass flow rate converter deal with the unit mismatches that property tables introduce.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering gauge pressures — the calculation needs absolute pressures at both ends. Using gauge values shrinks the pressure difference and shortens the tube.
- Guessing the bore — nominal capillary sizes vary between suppliers and tolerance on the internal diameter is significant. Measure or take the supplier's stated bore, because length depends on it very strongly.
- Using compressor capacity as the duty — the evaporator load is the number that sets refrigerant mass flow, and it is not the same figure as a compressor nameplate rating.
- Reading properties at the wrong temperature — density and viscosity are quoted for a state. Saturated liquid at 45 °C and saturated liquid at 30 °C are meaningfully different fluids for this purpose.
- Treating the result as final — the single-phase model ignores flashing, metastability and choking, all of which shorten the real tube. Always commission with a trial length and trim.
Related Free Tools From Arb Digital
Work the flow regime with the Reynolds number calculator and the friction factor calculator, then take the same physics into longer runs with the pipe flow calculator or into a sudden restriction with the orifice flow calculator. For the thermodynamics either side of the expansion, use the enthalpy calculator and the latent heat calculator, and size the room load with the AC BTU calculator. Unit housekeeping is handled by the viscosity converter and the mass flow rate converter. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
It is an order-of-magnitude starting point rather than a design figure. The calculation treats the refrigerant as a single-phase liquid over the whole tube, and a real capillary tube flashes partway along, which raises the pressure gradient sharply and shortens the required length. Expect to trim the real tube on a test rig.
Because refrigerant density, viscosity and refrigerating effect all depend on the saturation temperatures you are working between, so a single published figure per refrigerant would be wrong for most of the conditions readers actually type in. Taking the properties from a thermophysical database at your own conditions is the only defensible route.
Because velocity scales with the inverse square of diameter, and the friction pressure gradient scales with velocity squared divided by diameter. Combined, the required length varies with roughly the fourth to fifth power of bore, so a small diameter change swamps every other input on the page.
It is the condition where the two-phase mixture reaches sonic velocity at the tube outlet. Once that happens, lowering the evaporating pressure further does not increase mass flow at all, because information about the downstream pressure can no longer travel back up the tube.
Strongly, because there is no receiver to absorb a surplus. Too much charge backs liquid up into the condenser and raises head pressure; too little lets vapour reach the capillary inlet, which cuts mass flow sharply because vapour is far less dense than liquid. Charge is a design variable, not a top-up.
Cost, simplicity and reliability. It has no moving parts, needs no adjustment, and lets system pressures equalise on shutdown so a small hermetic compressor can restart easily. The price is that it is optimal at exactly one operating condition and approximate everywhere else.
Trimming to a balance point on an instrumented rig is the normal commissioning method, but it is work for a qualified refrigeration technician. Cutting into a charged system means recovering refrigerant, brazing and evacuating, all of which are regulated activities in most countries.
This tool is provided for educational and preliminary engineering use only. It is a simplified single-phase model and is not a design method for a refrigeration system. Refrigeration systems operate under pressure and refrigerant handling, recovery, brazing and charging are licensed or certified activities in most countries, including under Section 608 of the US Clean Air Act — see the US EPA stationary refrigeration and air conditioning programme. Have any real system sized, built and commissioned by a qualified refrigeration engineer or certified technician.
