These are the reference calculations our scientific calculator is checked against before every release. The table below is produced by running each one through the calculator itself.
✓74 of 74 pass.
How we compute
Answers are worked out in decimal to 40 significant digits and shown rounded half up to 15 (or 30).
Fractions, square roots and multiples of π are kept exact during the calculation, so exact angles give exact answers by rule. Nothing is rounded to zero for being small.
Whole numbers below 10³⁰ are shown in full. Larger or smaller numbers use scientific notation.
x% means x ÷ 100. For “a + b%” the calculator also offers the shop-style a × (1 + b/100).
Implied multiplication (2π, 2(3 + 4)) ranks with × and ÷, left to right, and the calculator says so on screen when it decides an answer.
Expected values were checked against an independent 80-digit computation and, for exact forms, by hand.
Everyday arithmetic
Calculation
Mode
Expected
Our answer
Result
Why it matters
0.1 + 0.2
DEG
0.3
0.3
✓ Pass
Binary floating point gives 0.30000000000000004.
1.1 × 1.1
DEG
1.21
1.21
✓ Pass
Binary floating point gives 1.2100000000000002.
1 ÷ 3
DEG
0.333333333333333 (exact 1/3)
0.333333333333333 (exact 1/3)
✓ Pass
A repeating decimal: the exact fraction is shown too.
2 ÷ 3
DEG
0.666666666666667 (exact 2/3)
0.666666666666667 (exact 2/3)
✓ Pass
The last shown digit rounds half up.
10 ÷ 4
DEG
2.5
2.5
✓ Pass
A terminating decimal needs no exact form.
7 − 10
DEG
−3
−3
✓ Pass
Negative results use a true minus sign.
123456789 × 987654321
DEG
121 932 631 112 635 269
121 932 631 112 635 269
✓ Pass
Every digit of an 18-digit product, exactly.
Order of operations
Calculation
Mode
Expected
Our answer
Result
Why it matters
2 + 3 × 4
DEG
14
14
✓ Pass
Multiplication before addition.
(2 + 3) × 4
DEG
20
20
✓ Pass
Brackets first.
−2²
DEG
−4
−4
✓ Pass
The power applies before the minus sign, as in textbooks.
(−2)²
DEG
4
4
✓ Pass
Brackets make the minus part of the base.
2^3^2
DEG
512
512
✓ Pass
Powers stack from the right: 2^(3^2).
2^−3
DEG
0.125
0.125
✓ Pass
A negative exponent needs no brackets.
6 ÷ 2(1 + 2)
DEG
9
9
✓ Pass
Implied multiplication ranks with × and ÷, left to right; the calculator shows “read as (6 ÷ 2)·(1 + 2)”.
1/2π
DEG
1.5707963267949 (exact π/2)
1.5707963267949 (exact π/2)
✓ Pass
Read as (1 ÷ 2)·π, and said so on screen.
2π
DEG
6.28318530717959 (exact 2π)
6.28318530717959 (exact 2π)
✓ Pass
A number next to π multiplies it.
Trigonometry in degrees
Calculation
Mode
Expected
Our answer
Result
Why it matters
sin(30)
DEG
0.5
0.5
✓ Pass
Exact by rule, not by rounding.
cos(60)
DEG
0.5
0.5
✓ Pass
Exact by rule.
sin(180)
DEG
0
0
✓ Pass
Many calculators show 1.2246E-16.
cos(90)
DEG
0
0
✓ Pass
Many calculators show 6.123E-17.
tan(45)
DEG
1
1
✓ Pass
Many calculators show 0.9999999999999999.
sin(45)
DEG
0.707106781186548 (exact √2/2)
0.707106781186548 (exact √2/2)
✓ Pass
The exact form is the textbook one.
sin(15)
DEG
0.258819045102521 (exact (√6 − √2)/4)
0.258819045102521 (exact (√6 − √2)/4)
✓ Pass
A less familiar exact value.
tan(60)
DEG
1.73205080756888 (exact √3)
1.73205080756888 (exact √3)
✓ Pass
Exact √3.
tan(90)
DEG
tan 90° is undefined
tan 90° is undefined
✓ Pass
Many calculators show 16331239353195370.
cos(120)
DEG
−0.5
−0.5
✓ Pass
The sign follows the quadrant.
Trigonometry in radians and grads
Calculation
Mode
Expected
Our answer
Result
Why it matters
sin(π)
RAD
0
0
✓ Pass
π is tracked exactly, so the sine is exactly 0.
cos(π)
RAD
−1
−1
✓ Pass
Exact.
sin(π/6)
RAD
0.5
0.5
✓ Pass
π/6 is 30°.
sin(1)
RAD
0.841470984807897
0.841470984807897
✓ Pass
A plain radian value, worked to 40 digits.
tan(π/2)
RAD
tan π/2 is undefined
tan π/2 is undefined
✓ Pass
Undefined, said plainly.
sin(100)
GRAD
1
1
✓ Pass
100 grad is a right angle.
cos(200)
GRAD
−1
−1
✓ Pass
200 grad is a half turn.
Inverse trigonometry
Calculation
Mode
Expected
Our answer
Result
Why it matters
sin⁻¹(0.5)
DEG
30
30
✓ Pass
Exactly 30, not 29.999999999999996.
cos⁻¹(0)
RAD
1.5707963267949 (exact π/2)
1.5707963267949 (exact π/2)
✓ Pass
The answer in radians, with its exact form.
tan⁻¹(1)
DEG
45
45
✓ Pass
Exact.
tan⁻¹(1)
RAD
0.785398163397448 (exact π/4)
0.785398163397448 (exact π/4)
✓ Pass
The same angle in radians.
sin⁻¹(2)
DEG
sin⁻¹ needs a value from −1 to 1
sin⁻¹ needs a value from −1 to 1
✓ Pass
No sine is greater than 1.
Hyperbolic functions
Calculation
Mode
Expected
Our answer
Result
Why it matters
sinh(1)
DEG
1.1752011936438
1.1752011936438
✓ Pass
Hyperbolic functions ignore the angle unit.
cosh(0)
DEG
1
1
✓ Pass
Exact.
tanh(1)
DEG
0.761594155955765
0.761594155955765
✓ Pass
Worked to 40 digits.
Logarithms
Calculation
Mode
Expected
Our answer
Result
Why it matters
log(1000)
DEG
3
3
✓ Pass
Exact powers of 10 give whole numbers.
log(0.001)
DEG
−3
−3
✓ Pass
And negative powers too.
ln(2)
DEG
0.693147180559945
0.693147180559945
✓ Pass
Natural logarithm.
ln(e)
DEG
1
1
✓ Pass
e is held to 40 digits, so this rounds to exactly 1.
log_2(8)
DEG
3
3
✓ Pass
Any base, exact when the answer is whole.
log_2(10)
DEG
3.32192809488736
3.32192809488736
✓ Pass
Any base, worked to 40 digits.
log(0)
DEG
log needs a number greater than 0
log needs a number greater than 0
✓ Pass
Explained, not “Math ERROR”.
Powers and roots
Calculation
Mode
Expected
Our answer
Result
Why it matters
√2
DEG
1.4142135623731 (exact √2)
1.4142135623731 (exact √2)
✓ Pass
Trailing zeros are trimmed: 1.41421356237310 shows as 1.4142135623731.
√16
DEG
4
4
✓ Pass
Perfect squares are exact.
∛27
DEG
3
3
✓ Pass
Perfect cubes are exact.
∛(−8)
DEG
−2
−2
✓ Pass
Odd roots of negative numbers are real.
2^0.5
DEG
1.4142135623731 (exact √2)
1.4142135623731 (exact √2)
✓ Pass
A power of one half is a square root.
(−8)^(1/3)
DEG
−2
−2
✓ Pass
Many calculators give an error or NaN here.
2^64
DEG
18 446 744 073 709 551 616
18 446 744 073 709 551 616
✓ Pass
Every digit; binary floating point shows 18446744073709552000.
2^100
DEG
1.26765060022823 × 10³⁰
1.26765060022823 × 10³⁰
✓ Pass
Past 10³⁰ the answer switches to scientific notation.
√(−4)
DEG
√ of a negative number needs complex numbers, coming later
√ of a negative number needs complex numbers, coming later
✓ Pass
Complex numbers are a later phase.
Factorials and combinations
Calculation
Mode
Expected
Our answer
Result
Why it matters
0!
DEG
1
1
✓ Pass
By definition.
25!
DEG
15 511 210 043 330 985 984 000 000
15 511 210 043 330 985 984 000 000
✓ Pass
All 26 digits, exactly.
30!
DEG
2.65252859812191 × 10³²
2.65252859812191 × 10³²
✓ Pass
Shown to 15 significant digits; the full value is behind “30 digits”.
52 nCr 5
DEG
2 598 960
2 598 960
✓ Pass
Five-card poker hands.
10 nPr 3
DEG
720
720
✓ Pass
Ordered arrangements.
2.5!
DEG
n! needs a whole number from 0 to 10 000
n! needs a whole number from 0 to 10 000
✓ Pass
Non-whole factorials (the gamma function) are a later phase.
Very large and very small numbers
Calculation
Mode
Expected
Our answer
Result
Why it matters
(1E−20 + 1) − 1
DEG
1 × 10⁻²⁰
1 × 10⁻²⁰
✓ Pass
Binary floating point loses the 10⁻²⁰ entirely and shows 0.
sin(1E−20)
RAD
1 × 10⁻²⁰
1 × 10⁻²⁰
✓ Pass
Tiny answers are never rounded away to 0.
1E300 × 1E300
DEG
1 × 10⁶⁰⁰
1 × 10⁶⁰⁰
✓ Pass
Binary floating point overflows to Infinity at about 1.8 × 10³⁰⁸.
10^(10^16)
DEG
Too large to show
Too large to show
✓ Pass
A number with ten quadrillion digits is reported, not shown.
1 ÷ 0
DEG
Can’t divide by zero
Can’t divide by zero
✓ Pass
Never “Infinity”.
Percent and mod
Calculation
Mode
Expected
Our answer
Result
Why it matters
50%
DEG
0.5
0.5
✓ Pass
x% means x ÷ 100.
200 + 10%
DEG
200.1
200.1
✓ Pass
Strictly 200 + 0.1; the calculator also offers “Meant 200 plus 10%? → 220”.
17 mod 5
DEG
2
2
✓ Pass
The remainder.
−7 mod 3
DEG
2
2
✓ Pass
The result takes the divisor’s sign: −7 = 3 × (−3) + 2.
Errors
Calculation
Mode
Expected
Our answer
Result
Why it matters
(2 + 3
DEG
Missing closing bracket
Missing closing bracket
✓ Pass
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