Unit Converter

Temperature Converter

Exact scales. Clear differences.

Convert a temperature

Readings and changes.

Conversion mode

Temperature value

Decimal, scientific value, fraction or mixed number. The reading must be at or above absolute zero.

From temperature scale

To temperature scale

Absolute readings use scale offsets. The tool checks the conventional absolute-zero boundary exactly without silently clamping your input.

View results

Precision and report

Display significant figures

Show exact target ratioShow calculation stepsShow all temperature scales

Decimal/scientific entry allows twenty significant digits, up to eighty characters and written exponents from negative thirty through thirty. Fractions allow one hundred digits per component and two hundred forty characters per field. Conversion factors do not add measurement precision.

Worked examples

Absolute reading in degrees celsius

T_t=20.0000000000\,{}^{\circ}\mathrm C

Scale offsets are included; the conventional absolute-zero boundary is enforced. Only display values are rounded.

Temperature conversion record

Source reading

T_s=68.0000000000\,{}^{\circ}\mathrm F

Absolute kelvin

T_K=293.150000000\,\mathrm K

Numerical mapping slope

A\approx0.555555555556

Numerical mapping offset

B\approx-17.7777777778

T_t=A T_s+B

Source scale: Degrees Fahrenheit. Target scale: Degrees Celsius. The mapping acts on numerical values in those scales. In the two-reading method, the source change is expressed in kelvin after the two absolute readings are normalized. Precision does not add information to the original measurements.

Reading in every supported scale

Every row describes the same absolute reading. Kelvin uses no degree sign. Copied text and CSV retain all four scales even when this table is hidden.

Absolute reading in four scales
Temperature scale	Reading
Degrees Celsius	$20.0000000000\,{}^{\circ}\mathrm C$
Degrees Fahrenheit	$68.0000000000\,{}^{\circ}\mathrm F$
Kelvin	$293.150000000\,\mathrm K$
Degrees Rankine	$527.670000000\,{}^{\circ}\mathrm R$

Step-by-step temperature conversion

1. Identify the absolute source reading
This is a location on a temperature scale. Its numerical zero is not necessarily absolute zero.
$T_s=68.0000000000\,{}^{\circ}\mathrm F$
2. Apply the source scale offset and interval size
The displayed coefficients act on numerical scale readings. Keep the exact offset before target conversion.
$T_K=\left(\frac{5}{9}\right)T_s+\left(\frac{45967}{180}\right)=293.150000000\,\mathrm K$
3. Apply the target scale offset
Subtract the target kelvin offset and divide by its kelvin interval size. Round only the displayed answer.
$T_t=\frac{T_K-b_t}{a_t}=20.0000000000\,{}^{\circ}\mathrm C$

What Can You Create?

Translate readings, intervals and observed temperature changes

Compare a thermometer reading

Convert a stated Celsius, Fahrenheit, kelvin or Rankine value while preserving the difference between its scale origin and interval size. Negative Celsius and Fahrenheit readings are supported when they remain above absolute zero.

Convert a rise or fall

Choose the interval mode for a known heating or cooling change. Its sign and magnitude are preserved without adding the offset that belongs only to absolute readings. A decrease remains negative in every scale.

Compare two independently labeled readings

Give the starting and ending readings separate scale selectors, normalize them before subtracting and keep their absolute kelvin values with the resulting change. Reverse the pair when you need the opposite direction.

Temperature conversion formulas and worked examples

Use an affine rule for absolute readings

Let $T_s$ and $T_t$ denote numerical readings in the source and target scales. Each scale has an exact kelvin interval coefficient $a$ and origin offset $b$ . First form $T_K=a_sT_s+b_s$ , then reverse the target definition. A single source-to-target multiplier is insufficient when the origins differ. The result record therefore shows both the numerical mapping slope and offset, rather than presenting temperature conversion as an ordinary mass or length factor.

T_t=\frac{a_sT_s+b_s-b_t}{a_t}=AT_s+B,\quad A=\frac{a_s}{a_t},\quad B=\frac{b_s-b_t}{a_t}

Example: the original Fahrenheit reading

For the original $68\,{}^{\circ}\mathrm F$ source, add the Fahrenheit-to-kelvin offset and scale the interval size to obtain $293.15\,\mathrm K$ . Subtract the Celsius origin to obtain $20\,{}^{\circ}\mathrm C$ . An equivalent direct formula subtracts $32$ from the Fahrenheit numerical reading and multiplies by $5/9$ . These operations act on the numerical readings and their stated units; do not interpret the intermediate written offset as a new measurement.

T_C=(68-32)\frac59=20,\qquad T_K=(68+459.67)\frac59=293.15

Example: an interval has no origin offset

When two readings are subtracted, their common origin cancels. A Celsius rise of $10$ degrees is a Fahrenheit rise of $18$ degrees; applying the absolute-reading formula would incorrectly produce $50$ . A Fahrenheit change of $-18$ degrees becomes a Celsius change of $-10$ degrees. Kelvin and Celsius intervals share the same size, as do Fahrenheit and Rankine intervals. The table headings and primary result explicitly identify a temperature change in these modes.

\Delta T_t=\frac{a_s}{a_t}\Delta T_s,\qquad \Delta T_F=\frac95\Delta T_C=18\,{}^{\circ}\mathrm F

Example: normalize two different scales before subtracting

Take a starting reading of $20\,{}^{\circ}\mathrm C$ and an ending reading of $86\,{}^{\circ}\mathrm F$ . Their normalized readings are $293.15\,\mathrm K$ and $303.15\,\mathrm K$ . Subtract start from end to find a rise of $10\,\mathrm K$ , then convert this interval to the target scale. Subtracting the raw source numbers would mix scale origins and interval sizes. Reversing the complete pair gives an equal-magnitude cooling interval, while equivalent readings such as $0\,{}^{\circ}\mathrm C$ and $32\,{}^{\circ}\mathrm F$ give exactly zero change.

\Delta T_K=T_{2,K}-T_{1,K}=303.15-293.15=10\,\mathrm K

Check absolute zero before rounding a display

In conventional absolute-reading mode the normalized result must satisfy $T_K\ge0$ . The exact boundary is $-273.15\,{}^{\circ}\mathrm C$ or $-459.67\,{}^{\circ}\mathrm F$ . No floating-point tolerance is used to accept a slightly smaller value. Conversely, a tiny positive kelvin value stays positive internally even if a rounded Celsius display lies very close to its lower boundary. Mathematical conversion, measurement uncertainty and the physical attainability of a particular reading are separate questions.

Why Users Love This Tool

Keep scale offsets and interval sizes auditable

Preserve the quantity meaning

Three modes distinguish a physical reading, a known change and a change between two readings.
Exact absolute-zero comparison applies only to physical readings.
Two-reading subtraction happens after independent normalization, preserving cooling and zero differences.

Retain the exact numerical model

Rational arithmetic keeps defined offsets and interval ratios exact before display rounding.
The mapping slope and offset remain visible beside normalized values.
Complete copy and CSV retain active context, all scale rows and hidden working.

Perfect For

Useful for lessons, technical readings and everyday comparisons

Students and teachers

Explain why Fahrenheit-to-Celsius conversion has an offset but interval conversion does not. Follow the source-to-kelvin and kelvin-to-target routes, or inspect the direct affine mapping beside the result.

Readers of lab and engineering records

Compare readings with different scale labels and retain the signed change. The tool converts numerical quantities; it does not determine sensor calibration, instrument uncertainty or a material response to the temperature.

Everyday temperature comparisons

Translate a stated weather, room or equipment reading using its actual scale. Presets illustrate arithmetic and do not substitute for a pressure-dependent phase-transition model or a use-specific safety threshold.

How It Works

How it works in three quick steps.

Decide whether the source is a reading or a change

Choose an absolute temperature reading for a thermometer value, a known temperature change for an already calculated rise or fall, or the two-reading mode to calculate a change. Enter a decimal, scientific value, simple fraction or proper mixed number. Identify the scale beside each input; the two-reading method gives each value its own independently selected scale.

Choose the destination and inspect the meaning

Select Celsius, Fahrenheit, kelvin or Rankine. Absolute readings must be at or above their conventional absolute-zero boundary, checked before rounding. Temperature changes can be positive, negative or zero. In the two-reading method, both physical readings are validated and converted to kelvin before subtracting start from end. The resulting table contains changes rather than absolute readings.

Review the exact working and retain the record

Choose display precision and optional exact ratio, all-scale table and calculation steps. Save the complete CSV, copy plain text or LaTeX, share validated active settings or print the chosen report. Exact swapping preserves whether the quantity is a reading or an interval; swapping a calculated two-reading result loads it as a known temperature change.

Download & Print

Save the meaning alongside the temperature number

Copy context or LaTeX working

The complete text record identifies whether the answer is an absolute reading or a signed change and retains active source scales. Mathematical copying supplies proper LaTeX steps. Clipboard failures are announced with a CSV fallback.

Download the exact conversion record

CSV includes every scale row, normalized readings, mapping coefficients, exact signed numerators and denominators and all generated steps, even when hidden on screen. Import long certificates as text if a spreadsheet would otherwise round their digits.

Print or save a readable PDF

Select the visible report sections and inspect the browser print preview. Editing controls and the supporting article are excluded. Long exact ratios receive a compact-print notice while complete digits remain available in text and CSV.

FAQ

Frequently Asked Questions

How do Celsius, Fahrenheit, kelvin and Rankine readings convert?

A reading needs both the interval size and the scale origin. Celsius maps to kelvin through

T_K=T_C+273.15

, Fahrenheit through

T_K=(T_F+459.67)5/9

, and Rankine through

T_K=5T_R/9

. The destination conversion reverses its own relationship. These numerical scale definitions are exact, although a thermometer reading may have limited accuracy. The calculator retains rational intermediate values and rounds only its presentation.

Why is a temperature difference converted without an offset?

When subtracting two readings on the same scale, its fixed origin cancels. Thus a change of

10\,{}^{\circ}\mathrm C

corresponds to

18\,{}^{\circ}\mathrm F

, while an absolute reading of

10\,{}^{\circ}\mathrm C

corresponds to

50\,{}^{\circ}\mathrm F

. Choose the change mode for an already known rise, fall or interval. A negative difference means cooling and does not imply that either underlying physical reading is below absolute zero.

What happens if I enter a reading below absolute zero?

This tool models conventional nonnegative thermodynamic readings. It rejects values below

0\,\mathrm K

, equivalent to

-273.15\,{}^{\circ}\mathrm C

-459.67\,{}^{\circ}\mathrm F

0\,{}^{\circ}\mathrm R

. The comparison uses the exact entered number before display rounding, so an invalid value is not silently clamped to the boundary. Signed temperature changes are different quantities and are allowed below zero. Specialized negative-temperature population models are outside this converter’s conventional reading mode.

Can the two readings use different temperature scales?

Yes. Enter a starting reading and ending reading with their own scale selectors. Each reading is first converted to kelvin and checked against absolute zero. The signed change is then

\Delta T_K=T_{2,K}-T_{1,K}

. For example, a start of

20\,{}^{\circ}\mathrm C

and an end of

86\,{}^{\circ}\mathrm F

give a rise of

10\,\mathrm K

, or

18\,{}^{\circ}\mathrm F

. Reversing the readings reverses the sign; equal physical readings give zero.

Does kelvin have a degree sign, and how does Rankine differ?

The SI unit is the kelvin, written

\mathrm K

without a degree symbol. Its interval size matches a Celsius degree, while its origin is absolute zero. Rankine also starts at absolute zero, but its degree interval matches Fahrenheit. Therefore

1\,{}^{\circ}\mathrm R

spans

5/9\,\mathrm K

. The converter retains the original four scale choices and labels Rankine explicitly, so it is not confused with another historical scale or with a temperature difference.

Are the freezing, boiling and room-temperature examples universal physical predictions?

They are numerical scale comparisons. The familiar pairs

0\,{}^{\circ}\mathrm C

and

32\,{}^{\circ}\mathrm F

, or

100\,{}^{\circ}\mathrm C

and

212\,{}^{\circ}\mathrm F

, demonstrate conversion arithmetic. Actual phase transitions depend on pressure, composition and experimental conditions, and a room-temperature example is an illustrative reading. The converter does not determine a boiling point, diagnose a body temperature, establish a food-safety limit or calibrate a sensor from those presets.

What do fractions, exact ratios and significant figures preserve?

Fractions and exact rational intermediate values preserve the numerical model you entered, including offsets that should cancel when two close readings are subtracted. The display supports three through twelve significant figures and marks rounded values as approximate. Exactness of the arithmetic does not improve the underlying thermometer measurement. A very small positive kelvin reading can display close to an absolute-zero Celsius value without becoming zero internally; exact swapping and CSV retain the distinction.

What do copying, CSV, sharing and PDF include?

Complete text copying and CSV retain the quantity kind, active inputs and scales, normalized kelvin values, mapping coefficients, exact signed numerators and denominators, every scale row and generated working, including hidden table or step sections. Share links retain validated inputs and display preferences. Printing saves the visible report through the browser dialog. Very long exact ratios receive a compact-print notice while their full digits remain in the copied record and CSV.

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About This Tool

About this Temperature Converter

The Toolarithm Temperature Converter handles the distinction that makes temperature different from ordinary factor-based unit conversion: most familiar scales do not share the same origin. It retains the original Fahrenheit-to-Celsius example and all four established scale identifiers. Defined interval ratios and offsets are evaluated as rational quantities, with rounding reserved for presentation. The result exposes a numerical mapping slope and offset so the conversion can be checked alongside its kelvin route. That numerical exactness describes the entered model rather than the calibration or uncertainty of an instrument.

Three entry methods serve different tasks. An absolute reading represents a location on the selected scale and is checked against conventional absolute zero. A known change represents an interval, so its sign is preserved and no scale-origin offset is added. The two-reading method accepts independently labeled starting and ending values, validates each physical reading and subtracts their normalized kelvin quantities. This avoids subtracting incompatible raw numbers and keeps a cooling interval separate from an impossible below-boundary reading. The complete report retains both original readings when that method is used.

Decimals, scientific syntax, fractions and proper mixed numbers are accepted within documented bounds. Three through twelve significant figures control the visible answer and scale table, while exact ratios, full copying and CSV retain the arithmetic certificates. Share links contain validated active inputs and display preferences. Exact swapping preserves the quantity kind; a two-reading result becomes a known interval rather than an unexplained new physical temperature. The page provides mathematical conversion and reproducible working. It does not infer a boiling point, heat transfer, material behavior, thermometer calibration, medical interpretation or operational safety limit from the converted number.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Conversion factors are normalized to canonical units and checked in both directions. Exact definitions and offset formulas are preferred over rounded lookup values.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

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