Tey Calculator

Calculate the net energy rate (Time-Energy Yield) of a process based on energy input, output, and cycle time.

Calculate TEY

Energy Projection Over Cycles

Cycles	Total Time (hours)	Total Eout (kWh)	Total Ein (kWh)	Total Net Energy (kWh)

Table showing projected total energy output, input, and net energy over an increasing number of cycles.

What is Time-Energy Yield (TEY)?

The Time-Energy Yield (TEY), in the context of this calculator, refers to the net energy produced or gained per unit of time, essentially the net power output of a system or process over its operational cycle. It quantifies how quickly a system generates more energy than it consumes.

A higher Time-Energy Yield (TEY) indicates a more efficient process in terms of net energy generation rate. It’s a crucial metric for evaluating the performance of energy-producing systems (like power plants, solar panels over time) or energy-consuming processes where net energy output or savings over time is important.

Anyone analyzing the energy balance and rate of net energy production of a system over time should use the Time-Energy Yield (TEY). This includes engineers, energy analysts, researchers, and those investing in energy technologies.

Common misconceptions about Time-Energy Yield (TEY) include confusing it with overall energy efficiency (which is a ratio of output to input without time per cycle) or EROEI (Energy Return on Energy Invested, which is total energy output over total energy input over the lifetime, not per unit time of a cycle). TEY specifically focuses on the *rate* of net energy gain during operational cycles.

Time-Energy Yield (TEY) Formula and Mathematical Explanation

The Time-Energy Yield (TEY), as calculated here (representing net power output), is determined using the following formula:

TEY = (E_out – E_in) / T_cycle

Where:

• TEY is the Time-Energy Yield or net power output (e.g., in kW).
• E_out is the energy output per cycle (e.g., in kWh).
• E_in is the energy input per cycle (e.g., in kWh).
• T_cycle is the duration of one cycle (e.g., in hours).

The term (E_out – E_in) represents the net energy gained per cycle. Dividing this by the time per cycle gives the average rate of net energy gain during that cycle.

The Total Net Energy over N cycles is: Total Net Energy = N * (E_out – E_in)

The Total Time over N cycles is: Total Time = N * T_cycle

Variables Table

Variable	Meaning	Unit	Typical Range
Eout	Energy Output per Cycle	kWh, J, MJ	0 to >1000
Ein	Energy Input per Cycle	kWh, J, MJ	0 to Eout or more
Tcycle	Time per Cycle	hours, s, min	>0
N	Number of Cycles	–	1 to >1,000,000
TEY	Time-Energy Yield (Net Power)	kW, W, MW	Varies widely

Practical Examples (Real-World Use Cases)

Example 1: Solar Panel System

A solar panel system generates an average of 5 kWh of electricity (E_out) during a 10-hour day (T_cycle), after accounting for the very small energy input to its inverter during that time, say 0.1 kWh (E_in).

• E_out = 5 kWh
• E_in = 0.1 kWh
• T_cycle = 10 hours

TEY = (5 – 0.1) / 10 = 4.9 / 10 = 0.49 kW. The system effectively provides a net power of 0.49 kW over the 10-hour cycle.

Example 2: Industrial Heating Process

An industrial furnace is used to heat material. It consumes 50 kWh (E_in) per 2-hour cycle (T_cycle). However, the process also recovers waste heat, generating 10 kWh (E_out) equivalent of energy that can be reused or is saved elsewhere per cycle.

• E_out = 10 kWh (recovered/saved)
• E_in = 50 kWh (consumed)
• T_cycle = 2 hours

TEY = (10 – 50) / 2 = -40 / 2 = -20 kW. The process has a net energy deficit rate of 20 kW. The Time-Energy Yield (TEY) is negative, indicating it’s a net energy consumer over time.

How to Use This Time-Energy Yield (TEY) Calculator

Here’s how to use the Time-Energy Yield (TEY) calculator:

1. Enter Energy Output per Cycle (E_out): Input the amount of energy produced or the useful energy output from one cycle of the process in kWh.
2. Enter Energy Input per Cycle (E_in): Input the amount of energy consumed or invested during one cycle in kWh.
3. Enter Time per Cycle (T_cycle): Input the duration of one complete cycle in hours.
4. Enter Number of Cycles (N): Input the total number of cycles you want to analyze for total energy figures.
5. View Results: The calculator automatically updates the Time-Energy Yield (TEY) (Net Power Output), Net Energy per Cycle, Total Net Energy, and Total Time.
6. Analyze Table and Chart: The table and chart show the progression of energy over the number of cycles entered.

A positive TEY means the process generates net energy over time; a negative TEY means it consumes net energy over time.

Key Factors That Affect Time-Energy Yield (TEY) Results

Several factors can influence the Time-Energy Yield (TEY):

• Efficiency of Conversion: How efficiently the input energy is converted to the desired output energy within the cycle. Higher efficiency generally leads to higher E_out for a given E_in. Check our efficiency metrics guide.
• Input Energy Source Quality: The quality and cost (both energy and financial) of the input energy can affect E_in.
• Cycle Duration (T_cycle): A shorter cycle time for the same net energy per cycle results in a higher TEY.
• System Degradation: Over time, the performance (E_out) of systems like solar panels or batteries can decrease, reducing TEY.
• Operational Time vs. Downtime: The number of effective cycles (N) over a period is reduced by downtime, affecting total net energy over long periods.
• Maintenance Energy Costs: Energy required for maintenance can be factored into E_in over many cycles, reducing the average TEY. Learn more about cycle analysis tools.

Frequently Asked Questions (FAQ)

What is a good Time-Energy Yield (TEY)?

A positive TEY is generally desirable for energy-generating systems, meaning it produces more energy than it consumes over time. The “goodness” depends on the application; for energy sources, a higher TEY is better. For consuming processes, a TEY closer to zero (or less negative) is better if energy recovery is involved.

Is TEY the same as EROEI?

No. EROEI (Energy Return on Energy Invested) is the ratio of total energy produced over the lifetime to the total energy invested to build, operate, and decommission. TEY, as calculated here, is the *rate* of net energy production (net power) during operational cycles. You can explore our energy ROI calculator for more on EROEI.

Can TEY be negative?

Yes, if the energy input per cycle (E_in) is greater than the energy output per cycle (E_out), the TEY will be negative, indicating a net energy consumption rate.

What units are used for TEY?

If energy is in kWh and time is in hours, TEY is in kW (kilowatts), representing power. If energy is in Joules and time in seconds, TEY is in Watts.

How does the number of cycles affect TEY?

The TEY (net power) itself is calculated per cycle and doesn’t change with the number of cycles. However, the Total Net Energy and Total Time scale directly with the number of cycles.

What if my cycle time is not constant?

This calculator assumes a constant average cycle time. If it varies significantly, you might need to calculate TEY for different phases or use an average T_cycle.

Does this calculator consider the energy to build the system?

No, this calculator focuses on the operational energy balance per cycle. The energy to build the system is considered in EROEI or Life Cycle Analysis. Our net energy explained page covers this.

Where can I apply TEY analysis?

It’s useful for renewable energy systems (solar, wind), energy storage (batteries during charge/discharge cycles), industrial processes, and any system with defined operational cycles and energy flows. See power output calculations for more.