gem-hunter

libqalculate

Tip

Visit the website at https://qalculate.github.io/ to see additional screenshots, read the manual, and download the latest version.

Requirements

Installation

API Documentation

Using the CLI program 'qalc'

Other Applications

Add-ons

Features

General

Symbolic calculations

Functions

Units

Variables and constants

Plots and graphs

Tip

For more details about the syntax, and available functions, units, and variables, please consult the manual (https://qalculate.github.io/manual/).

Examples (expressions)

Note

Semicolon can be replaced with comma in function arguments, if comma is not used as decimal or thousands separator.

Basic functions and operators

sqrt 4                        # = sqrt(4) = 4^(0.5) = 4^(1/2) = 2

sqrt(25; 16; 9; 4)            # = [5  4  3  2]

sqrt(32)                      # = 4 × √(2) (in exact mode)

cbrt(-27)                     # = root(-27; 3) = −3 (real root)

(-27)^(1/3)                   # ≈ 1.5 + 2.5980762i (principal root)

ln 25                         # = log(25; e) ≈ 3.2188758

log2(4)/log10(100)            # = log(4; 2)/log(100; 10) = 1

5!                            # = 1 × 2 × 3 × 4 × 5 = 120

5\2                           # = 5//2 = trunc(5 / 2) = 2 (integer division)

5 mod 3                       # = mod(5; 3) = 2

52 to factors                 # = 2^2 × 13

25/4 * 3/5 to fraction        # = 3 + 3/4

gcd(63; 27)                   # = 9

sin(pi/2) - cos(pi)           # = sin(90 deg) − cos(180 deg) = 2

sum(x; 1; 5)                  # = 1 + 2 + 3 + 4 + 5 = 15

sum(\i^2+sin(\i); 1; 5; \i)   # = 1^2 + sin(1) + 2^2 + sin(2) + … ≈ 55.176162

product(x; 1; 5)              # = 1 × 2 × 3 × 4 × 5 = 120
 
var1:=5                       # stores value 5 in variable var1
var1 * 2                      # = 10

sinh(0.5) where sinh()=cosh() # = cosh(0.5) ≈ 1.1276260

plot(x^2; -5; 5)              # plots the function y=x^2 from -5 to 5

Units

Tip

to can be replace with an arrow (➞ or ->).

5 dm3 to l                    # = 5 dm^3 to L = 5 L

20 miles / 2 h to km/h        # = 16.09344 km/h

1.74 to ft                    # = 1.74 m to ft ≈ 5 ft + 8.5039370 in

1.74 m to -ft                 # ≈ 5.7086614 ft

100 lbf * 60 mph to hp        # ≈ 16 hp

50 Ω * 2 A                    # = 100 V

50 Ω * 2 A to base            # = 100 kg·m²/(s³·A)

10 N / 5 Pa                   # = (10 N)/(5 Pa) = 2 m²

5 m/s to s/m                  # = 0.2 s/m

€500 - 20% to £               # ≈ £347.12

500 megabit/s * 2 h to b?byte # ≈ 419.09516 gibibytes

Physical constants

k_e / G * a_0
# = (CoulombsConstant / NewtonianConstant) × BohrRadius ≈ 7.126e9 kg·H·m^−1

ℎ / (λ_C * c)
# = planck ∕ (ComptonWavelength × SpeedOfLight) ≈ 9.1093837e-31 kg

5 ns * rydberg to c
# ≈ 6.0793194E-8c

atom(Hg; weight) + atom(C; weight) * 4 to g
# ≈ 4.129e-22 g

(G * planet(earth; mass) * planet(mars; mass))/(54.6e6 km)^2
# ≈ 8.58e16 N (gravitational attraction between earth and mars)

Uncertainty and interval arithmetic

Note

Results with interval arithmetic activated are shown in parenthesis.

sin(5±0.2)^2/2±0.3   # ≈ 0.460±0.088 (0.46±0.12)

(2±0.02 J)/(523±5 W) # ≈ 3.824±0.053 ms (3.825±0.075 ms)

interval(-2; 5)^2    # ≈ interval(−8.2500000; 12.750000) (interval(0; 25))

Tip

"±" can be replaced with "+/-".

Algebra

(5x^2 + 2)/(x - 3)                            # = 5x + 15 + 47/(x − 3)

(\a + \b)(\a - \b)                            # = 'a'^2 − 'b'^2

(x + 2)(x - 3)^3                              # = x^4 − 7x^3 + 9x^2 + 27x − 54

x^4 - 7x^3 + 9x^2 + 27x - 54 to factors       # = (x + 2)(x − 3)^3

cos(x)+3y^2 where x=pi; y=2                   # = 11

gcd(25x; 5x^2)                                # = 5x

1/(x^2+2x-3) to partial fraction              # = 1/(4x − 4) − 1/(4x + 12)

x+x^2+4 = 16                                  # x = 3 or x = −4

x^2/(5 m) - hypot(x; 4 m) = 2 m where x > 0   # x ≈ 7.1340411 m

cylinder(20cm; x) = 20l                       # x = (1 / (2π)) m ≈ 16 cm

asin(sqrt(x)) = 0.2                           # x = sin(0.2)^2 ≈ 0.039469503

x^2 > 25x                                     # x > 25 or x < 0

solve(x = y+ln(y); y)                         # = lambertw(e^x)

solve2(5x=2y^2; sqrt(y)=2; x; y)              # = 32/5

multisolve([5x=2y+32, y=2z, z=2x]; [x, y, z]) # = [−32/3  −128/3  −64/3]

dsolve(diff(y; x) - 2y = 4x; 5)               # = 6e^(2x) − 2x − 1

Calculus

diff(6x^2)                                    # = 12x

diff(sinh(x^2)/(5x) + 3xy/sqrt(x))            # = (2/5) × cosh(x^2) − sinh(x^2)/(5x^2) + (3y)/(2 × √(x))

integrate(6x^2)                               # = 2x^3 + C

integrate(6x^2; 1; 5)                         # = 248

integrate(sinh(x^2)/(5x) + 3xy/sqrt(x))       # = 2x × √(x) × y + Shi(x^2) / 10 + C

integrate(sinh(x^2)/(5x) + 3xy/sqrt(x); 1; 2) # ≈ 3.6568542y + 0.87600760

limit(ln(1 + 4x)/(3^x - 1); 0)                # = 4 / ln(3)

Matrices and vectors

[1, 2, 3; 4, 5, 6]                      # = [1  2  3; 4  5  6] (2×3 matrix)

1…5 = (1:5) = (1:1:5)                   # = [1  2  3  4  5]

(1; 2; 3) * 2 - 2                       # = [(1 × 2 − 2), (2 × 2 − 2), (3 × 2 − 2)] = [0  2  4]

[1 2 3].[4 5 6] = dot([1 2 3]; [4 5 6]) # = 32 (dot product)

cross([1 2 3]; [4 5 6])                 # = [−3 6 −3] (cross product)

[1 2 3; 4 5 6].*[7 8 9; 10 11 12]       # = [7  16  27; 40  55  72] (hadamard product)

[1 2 3; 4 5 6] * [7 8; 9 10; 11 12]     # = [58  64; 139  154] (matrix multiplication)

[1 2; 3 4]^-1                           # = inverse([1 2; 3 4]) = [−2  1; 1.5  −0.5]

Statistics

mean(5; 6; 4; 2; 3; 7)             # = 4.5

stdev(5; 6; 4; 2; 3; 7)            # ≈ 1.87

quartile([5 6 4 2 3 7]; 1)         # = percentile((5; 6; 4; 2; 3; 7); 25) ≈ 2.9166667

normdist(7; 5)                     # ≈ 0.053990967

spearman(column(load(test.csv); 1); column(load(test.csv); 2))
# ≈ −0.33737388 (depends on the data in the CSV file)

Time and date

10:31 + 8:30 to time           # = 19:01

10h 31min + 8h 30min to time   # = 19:01

now to utc                     # = "2020-07-10T07:50:40Z"

"2020-07-10T07:50CET" to utc+8 # = "2020-07-10T14:50:00+08:00"

"2020-05-20" + 523d            # = addDays(2020-05-20; 523) = "2021-10-25"

today - 5 days                 # = "2020-07-05"

"2020-10-05" - today           # = days(today; 2020-10-05) = 87 d

timestamp(2020-05-20)          # = 1 589 925 600

stamptodate(1 589 925 600)     # = "2020-05-20T00:00:00"

"2020-05-20" to calendars
# returns date in Hebrew, Islamic, Persian, Indian, Chinese, Julian, Coptic, and Ethiopian calendars

Number bases

52 to bin                               # = 0011 0100

52 to bin16                             # = 0000 0000 0011 0100

52 to oct                               # = 064

52 to hex                               # = 0x34

0x34 = hex(34)                          # = base(34; 16) = 52

523<<2&250 to bin                       # = 0010 1000

52.345 to float                         # ≈ 0100 0010 0101 0001 0110 0001 0100 1000

float(01000010010100010110000101001000) # = 1715241/32768 ≈ 52.345001

floatError(52.345)                      # ≈ 1.2207031e-6

52.34 to sexa                           # = 52°20′24″

1978 to roman                           # = MCMLXXVIII

52 to base 32                           # = 1K

sqrt(32) to base sqrt(2)                # ≈ 100000

0xD8 to unicode                         # = Ø

code(Ø) to hex                          # = 0xD8