Energy range-to-index mapLive point and endpoint line
Unit Converters
Energy Scale Calculator
Map an energy reading between input and target scales while exposing fraction, spans, endpoint checks, and extrapolation.
Boundary: this maps an energy range into a declared index. It is not a physical energy conversion and should not be used to infer state of charge without an approved endpoint model.
Mapped index-
Input fraction-
Energy span-
Output span-
Endpoint mapping-
Range state-
ENERGY SCALE
Show where the current energy sits inside a declared range
The scale chart distinguishes a linear display mapping from a physical conversion. The exact fraction and endpoints remain visible in the table.
| Element | Value | Unit | Meaning |
|---|
How to use
Map an energy amount into a defined operational index
Use this page for a dashboard index, state display, or controller coordinate when the endpoints have a documented physical meaning.
- Enter the live energy and unit from the source record.
- Define the input minimum and maximum from the approved range.
- Define output endpoints and name what the index represents.
- Review fraction and range state before using the index.
- Keep the energy value and mapped index together in the audit trail.
Scale fundamentals
Mapping is a coordinate transformation
Calculation method
Map the fraction, not the unit factor
r = (E − E₀)/(E₁ − E₀)z = z₀ + r(z₁ − z₀)valid iff 0 ≤ r ≤ 1The input energy unit stays consistent across E, E₀, and E₁; z is an index unit.
Default substitution
For E = 640 Wh, E₀ = 0 Wh, E₁ = 1,000 Wh and z = 0–100%, r = 0.64 and z = 64%.
Reconciliation
0 Wh maps to 0%; 1,000 Wh maps to 100%. Replacing the source unit with kWh must convert all three energy endpoints together.
Deep dive: battery state
State of charge is rarely linear in energy
Voltage sag, temperature, aging, and chemistry can make usable energy nonlinear. Use a validated battery model when the index controls protection or dispatch.
Deep dive: endpoint drift
Endpoints may move over life
A capacity fade changes the high endpoint. Keeping an old 1,000 Wh endpoint can make a healthy aged pack appear artificially low.
Deep dive: extrapolation
Out-of-range energy is a diagnostic
Do not clamp an over-capacity or negative value without recording the event; it may indicate a sensor, model, or process fault.
Cases, limits, and glossary
Use the index only for its declared question
Dashboard: 640 Wh maps to 64% of a 1,000 Wh declared range.
Thermal storage: a 0–500 kWh tank index may be useful for dispatch, but stratification and usable temperature limits belong in the endpoint model.
- Does not estimate nonlinear state-of-charge behavior.
- Does not correct sensor bias or capacity fade.
- Does not make an extrapolated value safe.
- Glossary: endpoint, fraction, index, span, capacity fade, extrapolation.
FAQ
Is this a physical energy conversion? No; it maps an energy range to a coordinate.
Can I use it for batteries? Only as a linear display approximation with validated endpoints.
Why convert all endpoints? A mixed-unit range produces a meaningless fraction.
What should an out-of-range result trigger? A sensor, model, or operating-condition review.
Result interpretation
Keep the physical energy and the mapped index side by side
The mapped index is a coordinate inside the declared energy range, not a new energy unit and not automatically a state-of-charge estimate. Fraction shows position in the signed input span, endpoint mapping checks the entered boundaries, and range state warns when the line is being extended beyond the approved model.
- A 64% fraction means the live energy is 64% through the declared span.
- A reversed output span can represent a valid reverse-acting indicator.
- An extrapolated index can be below 0 or above 100 and should not be silently clamped.
- Changing an endpoint changes the interpretation of every historical index value.
Detailed calculation process
Calculate the energy fraction before applying the index span
r = (E - E0) / (E1 - E0)z = z0 + r(z1 - z0)E, E0, and E1 share one energy unit; r is dimensionless; z uses the selected index label.
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| E | Live energy | 640 | Wh |
| E0 / E1 | Energy endpoints | 0 / 1,000 | Wh |
| z0 / z1 | Index endpoints | 0 / 100 | % |
| r | Energy fraction | (640 - 0) / (1,000 - 0) = 0.64 | dimensionless |
| z | Mapped index | 0 + 0.64(100 - 0) = 64 | % |
- Confirm the live energy and both endpoints use the same energy unit.
- Calculate the signed energy span: 1,000 - 0 = 1,000 Wh.
- Calculate the live offset: 640 - 0 = 640 Wh.
- Divide like units to obtain r = 0.64.
- Calculate the output span: 100 - 0 = 100 percentage points.
- Apply the fraction to obtain z = 64%.
- Classify the result as interpolation because 0 ≤ r ≤ 1.
- Reverse-check that both energy endpoints reproduce their paired index endpoints.
Evidence and endpoint control
Version the model when usable capacity changes
Record the source of minimum and maximum energy, battery or storage-system ID, temperature, age, chemistry, test rate, usable-versus-rated boundary, and endpoint revision. Historical indices are not comparable when capacity fade or operating policy changes the endpoints.
Scope and limitations
A linear index is not a physical storage model
- Voltage sag, temperature, aging, and nonlinear state estimation are not modeled.
- The calculator does not infer usable energy from nameplate capacity.
- Sensor bias, integration error, and capacity fade require separate evidence.
- Extrapolation is displayed but not certified as safe or meaningful.
- A dashboard index does not establish dispatch, protection, or warranty rules.
Practical examples
Indexes support different operating decisions
Storage dashboard: 640 Wh maps to 64% of a validated 0-1,000 Wh usable range; the raw Wh value remains available for audit.
Thermal store: 250 kWh may map to 50% of a 0-500 kWh dispatch range, but tank stratification and minimum delivery temperature remain outside the linear index.
Key terminology
Energy scale glossary
- Endpoint
- A physical energy boundary paired with an output coordinate.
- Span
- The signed difference between the high and low endpoints.
- Fraction
- The dimensionless position of live energy inside the span.
- Index
- A display coordinate derived from the declared range.
- Usable capacity
- Energy available within specified operating constraints.
- Capacity fade
- Reduction in available capacity as a storage system ages.
Frequently asked questions
Is the mapped index an energy conversion?
No. It is a coordinate transformation from an energy range to a separate output scale.
Can this percentage be used as battery state of charge?
Only as a validated linear approximation. Protection or dispatch needs a chemistry- and condition-specific state model.
Why must all energy endpoints use one unit?
The fraction divides differences; mixed units would make the position meaningless.
What should an extrapolated index trigger?
Review the sensor, integration model, endpoint revision, and operating condition before acting on it.
Important note
Before relying on this result
Validate endpoint meaning, linearity, and signal conditioning before control use.