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Energy Balance Calculator

Open system steady-state energy balance (SFEE): Q − Ws = ΔH + ΔKE + ΔPE with built-in steam table enthalpy data

Reviewed by Christopher FloiedPublished Updated

This free online energy balance calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Supports both metric (SI) and imperial units with built-in unit selection dropdowns on every input field, so you can work in whatever units your problem provides. Designed for engineering students and professionals working through coursework, design projects, or quick reference calculations.

Inlet Stream

Outlet Stream

Known Values

Energy Balance Results

h_in (kJ/kg)
83.60
h_out (kJ/kg)
334.40
ΔH (kW)
250.800
ΔKE (kW)
0.0000
ΔPE (kW)
0.0000
Solved: Heat Q (kW)
250.800
Heat added to system
Shaft Work Ws (kW)
0.000
Work input (pump/compressor)

Theory

Open System (SFEE): Q − Ws = ṁ_out·h_out − ṁ_in·h_in + ΔKE + ΔPE

ΔKE = ½ṁ_out·v_out² − ½ṁ_in·v_in² (kW)

ΔPE = ṁ_out·g·z_out − ṁ_in·g·z_in (kW)

Enthalpy uses built-in steam tables (for water/steam) or h = cp·T for other fluids.

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Energy Balance Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Energy Balance Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Energy Balance Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Energy Balance Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
  • Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
  • Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
  • Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
  • Use it in the field when a quick estimate is needed and a full engineering software package is not available.

About This Calculator

The Energy Balance Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Open system steady-state energy balance (SFEE): Q − Ws = ΔH + ΔKE + ΔPE with built-in steam table enthalpy data All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

The Theory Behind It

The steady-flow energy equation (SFEE) for an open system is Q − W_s = Δh + ΔKE + ΔPE, where Q is heat added per unit mass, W_s is shaft work per unit mass, Δh is enthalpy change from inlet to outlet, ΔKE is kinetic energy change, and ΔPE is potential energy change. For most process equipment (pumps, compressors, heat exchangers, reactors), kinetic and potential energy changes are negligible compared to enthalpy changes, simplifying to Q − W_s = Δh. For a heat exchanger with no shaft work: Q = Δh × ṁ, where ṁ is the mass flow rate. For a turbine or compressor with no heat transfer: W_s = −Δh × ṁ. For reactors with both heat transfer and chemical reaction: Q = ṁ_out · h_out − ṁ_in · h_in + reaction heat, where reaction heat = −ΔH_rxn × ξ (negative for exothermic, positive for endothermic). Enthalpies are referenced to a common state (usually 25°C reference); enthalpy of reaction at 25°C plus sensible heat to the actual temperature gives the correct value. The first law is applied to each unit operation in a process, and the results are combined to close the plant-wide energy balance. The calculator handles steady-state energy balances on 2-stream and 3-stream systems with built-in component property tables for common species.

Real-World Applications

  • Reactor cooling or heating requirements: compute the Q removed or added to maintain target temperature given reaction heat and flow conditions.
  • Heat exchanger duty: Q = ṁ·cp·ΔT for each side, used to size heat exchangers and specify cooling water or steam requirements.
  • Turbine and compressor sizing: compute shaft work from enthalpy change and mass flow rate; size drive motor or generator accordingly.
  • Plant-wide steam balance: track steam generation in boilers, use in process heating, condensation, and return as condensate; identify net steam demand.
  • Furnace and combustor design: compute fuel required to achieve target outlet temperature given feed conditions and heat loss.

Frequently Asked Questions

What is the steady-flow energy equation?

SFEE: Q − W_s = Δh + ΔKE + ΔPE (per unit mass flow). For most process equipment where KE and PE changes are small: Q − W_s = Δh. This is the first law of thermodynamics applied to a control volume with flowing streams. Q is heat added, W_s is shaft work done BY the system, Δh is enthalpy change from inlet to outlet.

Why use enthalpy instead of internal energy?

For open systems with flowing streams, the flow work p·v is automatically included in enthalpy (h = u + pv). This makes the energy balance simpler to write and avoids tracking the flow-work term separately. Internal energy (u) is used for closed systems where mass doesn't cross the boundary.

How do I include reaction heat?

Reaction contribution = −ΔH_rxn × ξ, where ΔH_rxn is the heat of reaction per mole at reference conditions (negative for exothermic) and ξ is the extent of reaction in moles. The total energy balance becomes: Q − W = (outlet enthalpy) − (inlet enthalpy) + (−ΔH_rxn × ξ). Use Hess's law to compute ΔH_rxn from heats of formation, or use tabulated values for common reactions.

When can I neglect kinetic and potential energy?

KE change is usually negligible for flow velocities below 100 m/s. For process streams in pipes at 1-10 m/s, KE is much smaller than enthalpy changes from heating/cooling. PE change is negligible for elevation changes less than 100 m. Exceptions: high-speed nozzles and diffusers (KE matters), tall distillation columns or tall reactors (PE can matter), pump calculations where static head is important.

What's the adiabatic flame temperature?

The maximum theoretical temperature reached if all combustion heat goes into heating the products (no heat loss, no radiation): Q = 0. Solve Δh_reactants→products = −ΔH_rxn for the temperature. Real flame temperatures are lower due to heat loss and dissociation at high temperatures. For methane in stoichiometric air: adiabatic flame temperature ≈ 2050°C; with excess air, lower.

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References & Further Reading