Number Range Mapping Calculator

Affine transformation · ℝ → ℝ

Map one directed scale onto another

Name the two endpoint pairs, place x on the source scale, and solve for the corresponding y without reordering your inputs.

t = (x − a) / (b − a)y = c + t(d − c)

Read the result

The result uses full precision before display rounding.

Mapped value · y77.00

25.0077.00

Interpolated inside the source scale25.00% from entered start toward entered end

Raw position · t: 0.25
Applied position: 0.25
Underlying line slope · m: 1.80
Underlying line intercept · q: 32.00

Underlying affine liney = 1.80x + 32.00

Show calculation trace

Find the signed fractional position in the source range.t = (25 − 0) / (100 − 0) = 0.25
Keep the raw position so values outside the source range follow the same line.applied t = 0.25
Apply the position to the signed target-range width.mapped = 32 + 0.25 × (212 − 32) = 77

Position correspondence

One parameter, two directed scales

start → end

Source entered order: 0 → 25.00 → 100.00
Target correspondence: 32.00 → 77.00 → 212.00
Normalized position: The same 25.00% position is used on both entered scales.

Numeric range transformation

Map one number range into another without mistaking it for a map

This mapping calculator performs an affine number transformation: it preserves a value's relative position inside one interval and expresses that position on a different interval. It does not geocode places, draw routes, or use geographic map data.

Step-by-step guide · Numeric range transformation

Define the source and destination intervals before entering the value

Core position: t = (x − source min) ÷ source span
Mapped value: target min + t × target span
Boundary choice: Clamp or extrapolate explicitly

Name what the source numbers represent
A sensor voltage, an animation frame, a test score, and a percentage may all use identical numbers but require different endpoints. Record the unit or label outside the arithmetic.
Choose a target scale with a clear purpose
For example, transform a 4–20 mA instrument signal to a declared engineering range, or translate a progress fraction into pixel coordinates. Do not imply precision that the source instrument never measured.
Check both endpoint images
The source minimum must map to the target minimum and the source maximum to the target maximum. Those two substitutions are a quick way to catch a reversed entry or copied endpoint.

Map one number range into another without mistaking it for a map: Writing the four endpoints first makes the transformation auditable and exposes unit or direction mistakes early.

A two-stage calculation preserves relative position

Start by measuring where the input sits between the source endpoints. For a source interval from 20 to 80 and an input of 35, the source span is 60 and the offset from the lower endpoint is 15. Dividing 15 by 60 gives t = 0.25. The second stage places that same quarter-position in the target interval. If the target runs from 0 to 100, the mapped answer is 25. This is an affine transformation because it can include both a scale change and a shift of origin.

The method also handles reversed intervals. Mapping from 100 down to 0 is valid because the target span is negative; a source midpoint becomes 50, while values nearer the source maximum move nearer the target minimum. Keep the endpoints in their intended order rather than sorting them, because direction carries meaning. When the values are geographic coordinates and the question is physical separation, use the coordinate distance calculator instead: range mapping and spatial distance answer entirely different questions.

Define the source and destination intervals before entering the value

Writing the four endpoints first makes the transformation auditable and exposes unit or direction mistakes early.

Name what the source numbers represent
A sensor voltage, an animation frame, a test score, and a percentage may all use identical numbers but require different endpoints. Record the unit or label outside the arithmetic.
Choose a target scale with a clear purpose
For example, transform a 4–20 mA instrument signal to a declared engineering range, or translate a progress fraction into pixel coordinates. Do not imply precision that the source instrument never measured.
Check both endpoint images
The source minimum must map to the target minimum and the source maximum to the target maximum. Those two substitutions are a quick way to catch a reversed entry or copied endpoint.

Clamping and extrapolation describe different policies

An input outside the source interval forces a decision; the formula cannot infer the real-world policy for you.

Clamp for bounded displays

Clamping replaces an input below the source minimum with that minimum and an input above the maximum with that maximum. Progress bars, color channels, and bounded controls often need this behavior so their outputs cannot leave the declared target range.

Extrapolate for a continuing linear assumption

Without clamping, t may be less than zero or greater than one. The output continues beyond the target endpoints at the same slope. That can be useful for a mathematical projection, but it is only defensible while the underlying relationship remains approximately linear.

Do not use extrapolation as a forecast

A mapped fuel gauge, price scale, or biological measurement can have physical limits and nonlinear behavior. For a trip budget, the fuel cost calculator models the relevant distance, economy, and price inputs rather than extending an unrelated scale.

Zero-width spans and early rounding are the main arithmetic traps

The source minimum and maximum cannot be equal. Their difference is the divisor, so a zero source span leaves relative position undefined rather than producing an infinite or arbitrary result.
A target span may be zero if every valid input is intentionally sent to one constant output. That is mathematically defined even though it discards all source variation.
Keep the unrounded t value through the target calculation. Rounding a fraction such as 1/3 before multiplication can move the final answer by much more than the chosen display precision.
If inputs have uncertainty, mapping scales that uncertainty by the absolute ratio of target span to source span. The displayed decimal places should follow the source data, not the calculator's ability to print digits.

Use the result inside a workflow with matching quantities

A mapping is most useful when the source and target meanings are written beside the result. An interface designer might map a temperature sensor's validated voltage range to a dial angle; an analyst might map a score band to a normalized index. If the task instead compares circular food sizes, the pizza value calculator uses area and unit price, not an arbitrary endpoint transformation.

Likewise, mapping an odometer reading onto a percentage does not reveal vehicle efficiency. The mileage calculator needs a distance difference and fuel added at the same refill. Selecting the narrow tool that represents the physical relationship prevents a neat numeric answer from being attached to the wrong question.

Important limitations

Number Range Mapping Calculator is limited to the finite inputs, modes, and outputs stated for the Linear number range mapping method. Check source range start, source range end, value to map, target range start, and target range end, validation messages, the equation, and the stated display precision before relying on mapped value, raw source position, applied position, and mapping slope.

This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.

Numeric range transformation

Map one number range into another without mistaking it for a map

Step-by-step guide · Numeric range transformation

Define the source and destination intervals before entering the value

Core position: t = (x − source min) ÷ source span
Mapped value: target min + t × target span
Boundary choice: Clamp or extrapolate explicitly

Name what the source numbers represent
A sensor voltage, an animation frame, a test score, and a percentage may all use identical numbers but require different endpoints. Record the unit or label outside the arithmetic.
Choose a target scale with a clear purpose
For example, transform a 4–20 mA instrument signal to a declared engineering range, or translate a progress fraction into pixel coordinates. Do not imply precision that the source instrument never measured.
Check both endpoint images
The source minimum must map to the target minimum and the source maximum to the target maximum. Those two substitutions are a quick way to catch a reversed entry or copied endpoint.

Map one number range into another without mistaking it for a map: Writing the four endpoints first makes the transformation auditable and exposes unit or direction mistakes early.

A two-stage calculation preserves relative position

Define the source and destination intervals before entering the value

Writing the four endpoints first makes the transformation auditable and exposes unit or direction mistakes early.

Name what the source numbers represent
A sensor voltage, an animation frame, a test score, and a percentage may all use identical numbers but require different endpoints. Record the unit or label outside the arithmetic.
Choose a target scale with a clear purpose
For example, transform a 4–20 mA instrument signal to a declared engineering range, or translate a progress fraction into pixel coordinates. Do not imply precision that the source instrument never measured.
Check both endpoint images
The source minimum must map to the target minimum and the source maximum to the target maximum. Those two substitutions are a quick way to catch a reversed entry or copied endpoint.

Clamping and extrapolation describe different policies

An input outside the source interval forces a decision; the formula cannot infer the real-world policy for you.

Clamp for bounded displays

Extrapolate for a continuing linear assumption

Do not use extrapolation as a forecast

Zero-width spans and early rounding are the main arithmetic traps

The source minimum and maximum cannot be equal. Their difference is the divisor, so a zero source span leaves relative position undefined rather than producing an infinite or arbitrary result.
A target span may be zero if every valid input is intentionally sent to one constant output. That is mathematically defined even though it discards all source variation.
Keep the unrounded t value through the target calculation. Rounding a fraction such as 1/3 before multiplication can move the final answer by much more than the chosen display precision.
If inputs have uncertainty, mapping scales that uncertainty by the absolute ratio of target span to source span. The displayed decimal places should follow the source data, not the calculator's ability to print digits.

Number Range Mapping Calculator

Map one directed scale onto another

Define the mapping

Read the result

One parameter, two directed scales

Map one number range into another without mistaking it for a map

Define the source and destination intervals before entering the value

Name what the source numbers represent

Choose a target scale with a clear purpose

Check both endpoint images

A two-stage calculation preserves relative position

Define the source and destination intervals before entering the value

Clamping and extrapolation describe different policies

Clamp for bounded displays

Extrapolate for a continuing linear assumption

Do not use extrapolation as a forecast

Zero-width spans and early rounding are the main arithmetic traps

Use the result inside a workflow with matching quantities

Important limitations

Map one directed scale onto another

Define the mapping

Read the result

One parameter, two directed scales

Map one number range into another without mistaking it for a map

Define the source and destination intervals before entering the value

Name what the source numbers represent

Choose a target scale with a clear purpose

Check both endpoint images

A two-stage calculation preserves relative position

Define the source and destination intervals before entering the value

Clamping and extrapolation describe different policies

Clamp for bounded displays

Extrapolate for a continuing linear assumption

Do not use extrapolation as a forecast

Zero-width spans and early rounding are the main arithmetic traps

Use the result inside a workflow with matching quantities