Unit Calculator

A free dimensional calculator. Evaluate expressions with units, automatic conversion, and dimensional checking — powered by the same engine as UnitSheet workbooks. No account needed.

Expression syntax

UnitSheet expressions combine numbers, units, arithmetic, comparisons, functions, and conversion. Workbook formulas use the same rules with a leading =.

Units are data

Dimensions travel with values through every formula.

25mi / 35min → mph → 42.86mph

Automatic conversion

Same-dimension add/subtract convert in place — results follow the first term's unit.

5m + 3ft → 5.9144m

Errors, not lies

Incompatible dimensions surface as errors, not quiet wrong answers.

5m + 3s → #UNIT

Comparisons

Compare quantities with the same dimension, or numbers and booleans.

10kg > 10lb → TRUE

Unit conversion

Convert with → or -> after the full expression.

8km → mi → 4.97mi

Derived units

Multiply and divide form new dimensions automatically.

10kW * 2.3h → kWh → 23kWh

Writing quantities

Write a number and a unit: 5m, 30s, 10kg, 10m/s, 10/s, 5/m.
Squared and cubed units can use Unicode or plain ASCII digits:
- 10m² or 10m2 → 10m²
- 10 m/s² or 10 m/s2 → 10m/s²
After a quantity, ^ means raise to a power, not “type a superscript in the unit.” So:
- 5 m² and 5 m2 are 5 square meters → 5m²
- 5 m^2 is 5 meters squared → 25m²
- 10 m/s² and 10 m/s2 are acceleration (10m/s²)
- 10 m/s^2 is (10 m/s)^2 → 100J/kg (same dimension as m²/s²)
Prefer m2 / m/s2 (or real superscripts) when you want the unit itself to be squared.
Inverse units use a leading slash (10/s, 5/m) rather than a negative exponent, so 5m-1m is subtraction.

Operators

Arithmetic: +, -, *, /. Same-dimension add/subtract convert automatically; multiply and divide form new dimensions (e.g. 25mi / 35min).
Comparisons: =, <>, <, >, <=, >=.
Convert with → or ->. On the right-hand side, caret form is fine for the target unit: 8km → mi, 25mi / 35min → mph, 10m*10m → ft^2.
Precedence (tightest first): ^, then * / /, then + / -, then →, then comparisons.
Functions use parentheses: SUM(1, 2, 3), AVERAGE(10m, 5ft), SIN(90°). Names are case-insensitive. Angles in trig functions convert to radians (SIN(90°) is 1; a bare number is already radians).

Function reference

93 Builtin formula functions, with more coming soon. Names are case-insensitive (sum ≡ SUM).

Math

ABS, SIGN, ROUND, ROUNDUP, ROUNDDOWN, FLOOR, CEILING, TRUNC, MOD, SQRT, POWER, EXP, LN, LOG, LOG10, PI, SIN, COS, TAN, ASIN, ACOS, ATAN, ATAN2, SINH, COSH, TANH, FACT, COMBIN, PERMUT, GCD, LCM, RAND, RANDBETWEEN, ERF, ERFC, GAMMA, PRODUCT, SUMPRODUCT, SUMSQ

Statistical

SUM, MAX, MIN, AVERAGE, MEDIAN, MODE, COUNT, COUNTA, STDEV, STDEVP, VAR, VARP, GEOMEAN, LARGE, SMALL, PERCENTILE, QUARTILE, CORREL, SLOPE, INTERCEPT, FORECAST, SUMIF, AVERAGEIF, COUNTIF

Logical

AND, OR, XOR, NOT, IF, IFERROR, IFS

Information

ISNUMBER, ISTEXT, ISQUANTITY, ISBLANK, ISERROR

Text

JOIN, SPLIT, LEFT, RIGHT, MID, LEN, TRIM, LOWER, UPPER, SEARCH, FIND, REPLACE, SUBSTITUTE, VALUE, TEXT

Lookup

INDEX, MATCH, XLOOKUP

Unit reference

286 units across 61 dimensions, with more coming soon.

Dimensionless [1]

1, ea, doz, gr, %, rad, °, arcmin, arcsec, sr

Time [T]

ps, ns, μs, ms, s, min, h, d, wk, yr

Frequency [T⁻¹]

Hz, Bq, /s, μHz, mHz, kHz, MHz, GHz, THz, PHz, EHz, rad/s, rpm

Time Squared [T²]

s²

Angular Acceleration [T⁻²]

rad/s², /s²

Length [L]

m, km, cm, mm, μm, nm, Å, pm, fm, am, in, mil, ft, yd, mi, nmi, au, ly, pc

Area [L²]

m², km², cm², mm², μm², nm², pm², fm², ac, ha, mi², yd², ft², in², L/100km

Volume [L³]

L, mL, μL, nL, pL, fL, aL, bbl, m³, cm³, mm³, μm³, nm³, pm³, fm³, am³, yd³, ft³, in³, gal, imp gal, qt, pt, cup, fl oz, tbsp, tsp

Wavenumber [L⁻¹]

/m, /cm

Inverse Area [L⁻²]

mpg, km/L

Mass [M]

kg, g, mg, μg, ng, pg, fg, ag, t, ton, lb, oz, st, slug, Da

Velocity [LT⁻¹]

m/s, km/h, mph, kt, ft/s, km/s

Acceleration [LT⁻²]

m/s², mph², kt², ft/s², km/s², g₀

Jerk [LT⁻³]

m/s³

Volume Flow Rate [L³T⁻¹]

m³/s, L/s, L/min, gpm, cfm

Linear Density [ML⁻¹]

kg/m, g/cm, lb/ft, oz/in, ton/yd, t/m

Area Density [ML⁻²]

kg/m², g/cm², lb/ft², oz/in², ton/yd², t/m²

Density [ML⁻³]

kg/m³, g/cm³, lb/ft³, oz/in³, ton/yd³, t/m³

Moment of Mass [LM]

kg⋅m, lb⋅ft

Moment of Inertia [ML²]

kg⋅m², lb⋅ft², lb⋅in²

Mass Flow Rate [MT⁻¹]

kg/s, lb/s, oz/s, ton/s, t/s, ton/h

Momentum [LMT⁻¹]

kg⋅m/s

Force [LMT⁻²]

N, kN, dyn, lbf, kgf

Surface Tension [MT⁻²]

N/m

Pressure [ML⁻¹T⁻²]

Pa, hPa, kPa, MPa, bar, mbar, atm, Torr, mmHg, inHg, psi, psf, J/m³

Dynamic Viscosity [MT⁻¹L⁻¹]

Pa⋅s, P, cP

Kinematic Viscosity [L²T⁻¹]

m²/s

Angular Momentum [ML²T⁻¹]

J⋅s, kg⋅m²/s

Energy [ML²T⁻²]

J, kJ, eV, cal, kcal, erg, Btu, ft⋅lbf, Wh, kWh, MWh, GWh, TWh, PWh

Power [ML²T⁻³]

W, kW, MW, GW, TW, PW, EW, hp, Btu/h

Irradiance [MT⁻³]

W/m²

Specific Energy [L²T⁻²]

J/kg, Sv, Gy

Current [I]

A, mA, μA, nA, pA, fA

Electric Charge [TI]

C, mC, μC, nC, pC, fC, aC

Electric Charge Density [TIL⁻³]

C/m³

Electric Potential [ML²I⁻¹T⁻³]

V, mV, kV, MV

Electric Field [LMI⁻¹T⁻³]

V/m

Electric Reluctance [T²I²M⁻¹L⁻²]

A/Wb

Conductance [I²T³M⁻¹L⁻²]

S

Conductivity [I²T³M⁻¹L⁻³]

S/m

Capacitance [I²T⁴M⁻¹L⁻²]

F, μF, nF, pF

Inductance [ML²T⁻²I⁻²]

H, mH, μH

Magnetic Flux [ML²I⁻¹T⁻²]

Wb

Magnetic Flux Density [MI⁻¹T⁻²]

T, G

Magnetic Field [IL⁻¹]

A/m

Resistance [ML²I⁻²T⁻³]

Ω, kΩ, MΩ

Resistivity [ML³I⁻²T⁻³]

Ω⋅m

Entropy [ML²Θ⁻¹T⁻²]

J/K

Specific Entropy [L²Θ⁻¹T⁻²]

J/(kg⋅K)

Thermal Conductivity [LMΘ⁻¹T⁻³]

W/(m⋅K)

Heat Transfer Coefficient [MΘ⁻¹T⁻³]

W/(m²⋅K)

Temperature [Θ]

K, °C, °F, °Ré, °R, °D

Chemical Amount [N]

mol, mmol, μmol, nmol, pmol, fmol, amol

Catalytic Activity [NT⁻¹]

kat

Per Mole [N⁻¹]

/mol

Molar Concentration [NL⁻³]

mol/m³, mol/L

Molar Energy [ML²N⁻¹T⁻²]

J/mol

Molar Entropy [ML²Θ⁻¹N⁻¹T⁻²]

J/(mol⋅K)

Molar Charge [TIN⁻¹]

C/mol

Luminous Intensity [J]

cd, lm, mcd, μcd, ncd, pcd, fcd, acd

Illuminance [JL⁻²]

lx