Free Scientific Calculator Online (with DEG/RAD Guide)

Use the free scientific calculator below for trigonometry, logarithms, powers, roots, factorials and very large or very small numbers. It works on phones and computers: tap the keys or type directly, and the answer updates as you type.

Quick guide to the keys

Key	What it does	Example	Result
sin, cos, tan	Trig functions (in DEG or RAD mode)	sin(30) in DEG	0.5
sin⁻¹, cos⁻¹, tan⁻¹	Inverse trig (angle from a ratio)	sin⁻¹(0.5) in DEG	30
ln	Natural log (base \( e \))	ln(e²)	2
log	Log base 10	log(1000)	3
x², x³, xʸ	Powers	2^10	1024
√, ∛	Square and cube roots	∛27	3
n!	Factorial	5!	120
1/x	Reciprocal	4^(−1)	0.25
EXP	Times ten to a power	6.02×10^23	\( 6.02\times10^{23} \)
π, e	Constants	2π	6.28318530718
Ans	Previous answer	7 + Ans	uses the last result

DEG vs RAD: the most common calculator mistake

Angles can be measured in degrees (a full turn is 360°) or radians (a full turn is \( 2\pi \)). The DEG/RAD button at the top-left of the display switches between them.

• In DEG mode, \( \sin 30 = 0.5 \).
• In RAD mode, \( \sin 30 \approx -0.988 \), because 30 radians is almost five full turns.

Rule of thumb: use DEG for triangle and geometry problems stated in degrees. Use RAD for calculus: derivatives like \( \frac{d}{dx}\sin x = \cos x \) are only true in radians (see derivative of tan x and limit of sin x / x). In RAD mode, \( \sin\frac{\pi}{6} = 0.5 \).

Converting between degrees and radians

A full turn is \( 360° = 2\pi \) radians, so \( 180° = \pi \). That gives two conversion rules:

• Degrees to radians: multiply by \( \frac{\pi}{180} \). For example, \( 45° = \frac{\pi}{4} \approx 0.7854 \).
• Radians to degrees: multiply by \( \frac{180}{\pi} \). For example, \( \frac{2\pi}{3} = 120° \), and 1 radian is about 57.296°.

You can type the conversion directly: 1.2*180/π gives about 68.755, so 1.2 radians is roughly 68.8°. A quick sanity check is that angles in radians are usually small numbers (a right angle is only about 1.571), while degree measures for the same angles are much larger.

Inverse trig keys answer in whichever mode is active. In DEG mode, sin⁻¹(0.5) returns 30; in RAD mode it returns about 0.5236, which is \( \frac{\pi}{6} \). Both are correct, just in different units.

In DEG mode this calculator gives exact answers at special angles: \( \sin 180° = 0 \), \( \cos 90° = 0 \), and \( \tan 90° \) is reported as undefined rather than a huge rounding error.

Order of operations

Order of operations decides which part of an expression is worked out first. The calculator follows the standard order: brackets, powers and roots, multiplication and division, then addition and subtraction.

• \( 3\times4^2 = 3\times16 = 48 \), but \( (3\times4)^2 = 144 \).
• \( -3^2 = -9 \) (the power is applied first), while \( (-3)^2 = 9 \). Use brackets, or the (−) key inside brackets, when squaring a negative number.
• Implicit multiplication works: 2π, 3sin(30) and 2(4+1) all mean what you’d expect.
• Squared trig functions need brackets in the right place. \( \sin^2 30° \) means \( (\sin 30°)^2 = 0.25 \), so type sin(30)^2. Typing sin(30^2) takes the sine of 900°, which is 0.
• Fractions with more than one term on top or bottom need brackets around each part. \( \frac{4 + 6}{2 + 3} = 2 \) must be typed (4+6)/(2+3); without brackets, 4+6/2+3 gives 10.
• When an expression could be read two ways, add brackets. They never hurt, and they make the calculator do exactly what you intend.

Logarithms: ln vs log

• ln is the natural logarithm, base \( e \approx 2.71828 \). It’s the one used in calculus, as in the derivative of ln x.
• log on this calculator is base 10, so \( \log 1000 = 3 \) and \( \log 2 \approx 0.30103 \).
• The log key enters lg( in the display, which means base 10. If you type with a keyboard, log( also means base 10 here, just as on a handheld scientific calculator; use ln( for the natural log.
• For any other base, use the change-of-base rule: \( \log_b x = \frac{\ln x}{\ln b} \). For example, \( \log_2 8 = \frac{\ln 8}{\ln 2} = 3 \).

Scientific notation with EXP

The EXP key enters “×10^”. To type Avogadro’s number, press 6.02, EXP, 23. Very large and very small answers are shown the same way, such as \( 1.204\times10^{24} \). Negative exponents work too: \( 10^{-3} = 0.001 \).

Scientific notation writes a number as a value between 1 and 10 times a power of 10. The exponent counts how many places the decimal point moves: \( 6.371\times10^6 = 6{,}371{,}000 \), and \( 3.2\times10^{-4} = 0.00032 \). Positive exponents mean big numbers; negative exponents mean small ones, not negative ones.

Multiplying and dividing is easy to check by hand. Multiply the front numbers and add the exponents: \( (3\times10^8)(2\times10^{-3}) = 6\times10^5 \). Divide the front numbers and subtract the exponents: \( \frac{6.4\times10^6}{1.6\times10^{-3}} = 4\times10^9 \). If your calculator answer’s exponent doesn’t match this quick estimate, something was typed wrong.

Two keying mistakes cause most scientific-notation errors:

• Typing 10 before EXP. EXP already means “×10^”, so 10 EXP 5 is \( 10\times10^5 = 10^6 \). For \( 10^5 \), type 1 EXP 5, or use 10^5.
• Dividing by a number in scientific notation without brackets. EXP types “×10^” into the expression, so the order of operations still applies. Type 6.4×10^6/(1.6×10^(-3)) with brackets around the divisor. Without them, the calculator divides by 1.6 and then multiplies by \( 10^{-3} \).

Some calculators and spreadsheets show scientific notation as E notation, so 9.468E15 means \( 9.468\times10^{15} \).

Handy examples

1. Hypotenuse: \( \sqrt{3^2 + 4^2} = 5 \)
2. Angle of a ramp rising 1 m over 2 m: \( \tan^{-1}(0.5) \approx 26.565° \)
3. Compound growth: \( 1000\times1.05^{10} \approx 1628.89 \)
4. Arrangements of 6 books: \( 6! = 720 \)
5. pH from concentration \( 3.2\times10^{-4} \): \( -\log(3.2\times10^{-4}) \approx 3.49 \)
6. Height of a tree seen at a 35° angle of elevation from 50 m away: \( 50\tan 35° \approx 35.01 \) m (DEG mode).
7. Doubling time at 5% continuous growth: \( \frac{\ln 2}{0.05} \approx 13.86 \) years.
8. Earth’s circumference from its radius \( 6.371\times10^6 \) m: \( 2\pi r \approx 4.003\times10^7 \) m.

Worked science examples

These show the full reasoning, including which mode to use and how to type each expression.

Projectile range. A ball is launched at 20 m/s at 30° above the ground. Ignoring air resistance, the range is \( R = \frac{v^2\sin 2\theta}{g} \) with \( g = 9.8 \) m/s². The angle is in degrees, so switch to DEG and type 20^2*sin(2*30)/9.8. The answer is about 35.35 m. In RAD mode the same keystrokes give a meaningless result, because the calculator would take the sine of 60 radians.

How far light travels in a year. Light moves at about \( 3.00\times10^8 \) m/s, and a year is about \( 3.156\times10^7 \) s. Type 3 EXP 8 × 3.156 EXP 7 to get about \( 9.468\times10^{15} \) m, one light-year. Estimate first: \( 3\times3 = 9 \) and \( 8 + 7 = 15 \), so the answer should be near \( 9\times10^{15} \).

Radioactive decay. Carbon-14 has a half-life of 5730 years. The amount left from 100 g after 2000 years is \( 100\times0.5^{2000/5730} \). Put the whole exponent in brackets, 100*0.5^(2000/5730), to get about 78.51 g. Leaving out the brackets would raise 0.5 to the power 2000 and then divide by 5730.

Sound level in decibels. The level of a sound with intensity \( 10^{-5} \) W/m² is \( 10\log\frac{I}{I_0} \) with \( I_0 = 10^{-12} \). Type 10×, press the log key, then enter 10^(-5)/10^(-12)) to get 70 dB; the brackets around each power keep the division correct. Here the log must be base 10, not ln.

Factorials grow fast. \( 20! = 2{,}432{,}902{,}008{,}176{,}640{,}000 \), about \( 2.43\times10^{18} \). This is why counting problems quickly produce answers in scientific notation.

When you need more than a calculator

A scientific calculator gives numbers. For formulas and full working, try the step-by-step solver for derivatives, integrals and limits, or the simple calculator for everyday sums.

To see what a function looks like rather than a single value, plot it with the graphing calculator. For symbolic derivatives with every step shown, use the derivative calculator. If you’re curious how a calculator finds \( \sin x \) or \( e^x \) in the first place, the answer is series like the ones in our Taylor series guide, and the calculus concepts guide explains the ideas behind them.

Practice problems

Try these with the calculator above (DEG mode unless stated).

1. \( \cos 60° \)
2. \( \log 0.01 \)
3. \( \sqrt[3]{125} + 4! \)

Answers: (1) \( 0.5 \); (2) \( -2 \); (3) \( 29 \).

FAQ

Why does my calculator give sin 30 = −0.988?

It’s in radian mode. Switch to DEG to get 0.5.

Is log the same as ln?

No. On this calculator, log is base 10 and ln is base \( e \). Some calculus textbooks write \( \log \) for the natural log, so check your course’s convention.

Can I use this calculator on exams?

This is an online tool; exam rules vary. It’s ideal for homework, checking answers and learning how each function behaves.

How do I convert degrees to radians?

Multiply by \( \frac{\pi}{180} \). To go back, multiply by \( \frac{180}{\pi} \). For example, 90° is \( \frac{\pi}{2} \approx 1.5708 \) radians.

What does an answer like 1.2E-7 mean?

It’s E notation for \( 1.2\times10^{-7} \), or 0.00000012. The number after the E is the power of 10.

Why do I get an error for sin⁻¹(2) or log(−5)?

Those inputs are outside the function’s domain. Sine is never larger than 1, so no angle has a sine of 2, and logarithms are only defined for positive numbers.

Does it work offline?

Once the page has loaded, all calculations run in your browser. Nothing you type is sent to a server.

Further reading

• Order of operations (Wikipedia) — the PEMDAS and BODMAS conventions, and how calculators handle the ambiguous cases.
• Scientific notation (Wikipedia) — normalized form, E notation and significant figures in detail.
• Radian (Wikipedia) — where the radian comes from and why it’s the natural unit for calculus.