$\bf{
2.56 \pm0.04}$

OUR FIT
Assuming inverted mass hierarchy

$\bf{
2.51 \pm0.05}$

OUR FIT
Error includes scale factor of 1.1.
Assuming normal mass hierarchy

$2.54$ $\pm0.08$ 
^{ 1} 

T2K 
$2.51$ $\pm0.08$ 
^{ 1} 

T2K 
$2.67$ $\pm0.11$ 


NOVA 
$2.72$ $\pm0.11$ 


NOVA 
$2.45$ $\pm0.06$ $\pm0.06$ 
^{ 2} 

DAYA 
$2.56$ $\pm0.06$ $\pm0.06$ 
^{ 2} 

DAYA 
$2.56$ ${}^{+0.21}_{0.23}$ ${}^{+0.12}_{0.13}$ 
^{ 3} 

RENO 
$2.69$ ${}^{+0.23}_{0.21}$ ${}^{+0.13}_{0.12}$ 
^{ 3} 

RENO 
$2.72$ ${}^{+0.19}_{0.20}$ 
^{ 4} 

ICCB 
$2.73$ ${}^{+0.21}_{0.18}$ 
^{ 4} 

ICCB 
$2.37$ $\pm0.09$ 
^{ 5} 

MINS 
$2.41$ ${}^{+0.09}_{0.12}$ 
^{ 5} 

MINS 
• • • We do not use the following data for averages, fits, limits, etc. • • • 
$2.53$ ${}^{+0.15}_{0.13}$ 


T2K 
$2.55$ ${}^{+0.33}_{0.27}$ 


T2K 
$2.55$ ${}^{+0.08}_{0.08}$ 


T2K 
$2.63$ ${}^{+0.08}_{0.08}$ 


T2K 
$2.51$ ${}^{+0.29}_{0.25}$ 
^{ 6} 

T2K 
$2.52$ ${}^{+0.20}_{0.18}$ 
^{ 7} 

NOVA 
$2.56$ $\pm0.19$ 
^{ 7} 

NOVA 
$\text{2.0  5.0}$ 
^{ 8} 

OPER 
$2.37$ $\pm0.11$ 
^{ 9} 

DAYA 
$2.47$ $\pm0.11$ 
^{ 9} 

DAYA 
$2.51$ $\pm0.10$ 
^{ 10} 

T2K 
$2.56$ $\pm0.10$ 
^{ 10} 

T2K 
$2.54$ ${}^{+0.19}_{0.20}$ 
^{ 11} 

DAYA 
$2.64$ ${}^{+0.20}_{0.19}$ 
^{ 11} 

DAYA 
$2.48$ ${}^{+0.05}_{0.07}$ 
^{ 12} 

FIT 
$2.38$ ${}^{+0.06}_{0.05}$ 
^{ 12} 

FIT 
$2.457$ $\pm0.047$ 
^{ 13}^{, 14} 

FIT 
$2.449$ ${}^{+0.047}_{0.048}$ 
^{ 13} 

FIT 
$2.3$ ${}^{+0.6}_{0.5}$ 
^{ 15} 

ICCB 
$2.44$ ${}^{+0.17}_{0.15}$ 
^{ 16} 

T2K 
$2.41$ ${}^{+0.09}_{0.10}$ 
^{ 17} 

MINS 
$\text{2.2  3.1}$ 
^{ 18} 

T2K 
$2.62$ ${}^{+0.31}_{0.28}$ $\pm0.09$ 
^{ 19} 

MINS 
$\text{1.35  2.55}$ 
^{ 20}^{, 21} 

MINS 
$\text{1.4  5.6}$ 
^{ 20}^{, 22} 

MINS 
$\text{0.9  2.5}$ 
^{ 20}^{, 22} 

MINS 
$\text{1.8  5.0}$ 
^{ 23} 

ANTR 
$\text{1.3  4.0}$ 
^{ 24} 

SKAM 
$2.32$ ${}^{+0.12}_{0.08}$ 


MINS 
$3.36$ ${}^{+0.46}_{0.40}$ 
^{ 25} 

MINS 
$\text{< 3.37}$ 
^{ 26} 

MINS 
$\text{1.9  2.6}$ 
^{ 27} 

SKAM 
$\text{1.7  2.7}$ 
^{ 27} 

SKAM 
$2.43$ $\pm0.13$ 


MINS 
$\text{0.07  50}$ 
^{ 28} 

MINS 
$\text{1.9  4.0}$ 
^{ 29}^{, 30} 

K2K 
$\text{2.2  3.8}$ 
^{ 31} 

MINS 
$\text{1.9  3.6}$ 
^{ 29} 

K2K 
$\text{0.3  12}$ 
^{ 32} 

SOU2 
$\text{1.5  3.4}$ 
^{ 33} 

SKAM 
$\text{0.6  8.0}$ 
^{ 34} 

MCRO 
$1.9\text{ to }3.0 $ 
^{ 35} 

SKAM 
$\text{1.5  3.9}$ 
^{ 36} 

K2K 
$\text{0.25  9.0}$ 
^{ 37} 

MCRO 
$\text{0.6  7.0}$ 
^{ 38} 

MCRO 
$\text{0.15  15}$ 
^{ 39} 

SOU2 
$\text{0.6  15}$ 
^{ 40} 

MCRO 
$\text{1.0  6.0}$ 
^{ 41} 

MCRO 
$\text{1.0  50}$ 
^{ 42} 

SKAM 
$\text{1.5  15.0}$ 
^{ 43} 

SKAM 
$\text{0.7  18}$ 
^{ 44} 

SKAM 
$\text{0.5  6.0}$ 
^{ 45} 

SKAM 
$\text{0.55  50}$ 
^{ 46} 

KAMI 
$\text{4  23}$ 
^{ 47} 

KAMI 
$\text{5  25}$ 
^{ 48} 

KAMI 
^{1}
Supersedes ABE 2017C.

^{2}
AN 2017A report results from combined rate and spectral shape analysis of 1230 days of data taken with the Daya Bay reactor experiment. The data set contains more than $2.5 \times 10^{6}$ inverse betadecay events with neutron capture on ${}^{}\mathrm {Gd}$. The fit to the data gives $\Delta {}^{2}_{ee}=0.00250$ $\pm0.00006$ $\pm0.00006$ eV. Supersedes AN 2015 .

^{3}
CHOI 2016 reports result of the RENO experiment from a rate and shape analysis of 500 days of data. A simultaneous fit to $\theta _{13}$ and $\Delta $m${}^{2}_{ee}$ yields $\Delta $m${}^{2}_{ee}$ = $0.00262$ ${}^{+.00021}_{.00023}{}^{+.00012}_{.00013}$ eV. We convert the results to $\Delta $m${}^{2}_{32}$ using PDG 2014 values of sin$^2({{\mathit \theta}_{{12}}})$ and $\Delta $m${}^{2}_{21}$.

^{4}
AARTSEN 2015A obtains this result by a threeneutrino oscillation analysis using $10  100$ GeV muon neutrino sample from a total of 953 days of measurements with the lowenergy subdetector DeepCore of the IceCube neutrino telescope.

^{5}
ADAMSON 2014 uses a complete set of accelerator and atmospheric data. The analysis combines The analysis combines the ${{\mathit \nu}_{{\mu}}}$ disappearance and ${{\mathit \nu}_{{e}}}$ appearance data using threeneutrino oscillation fit. The fit results are obtained for normal and inverted mass ordering assumptions.

^{6}
ABE 2016D reports oscillation results using ${{\overline{\mathit \nu}}_{{\mu}}}$ disappearance in an offaxis beam.

^{7}
Superseded by ADAMSON 2017A.

^{8}
AGAFONOVA 2015A result is based on 5 ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{\tau}}}$ appearance candidates with an expected background of $0.25$ $\pm0.05$ events. The best fit is for $\Delta $m${}^{2}_{32}=3.3 \times 10^{3}$ eV${}^{2}$.

^{9}
AN 2015 uses all eight identical detectors, with four placed near the reactor cores and the remaining four at the far hall to determine prompt energy spectra. The results correspond to the exposure of $6.9 \times 10^{5}$ GW$_{th}$tondays. They derive $\Delta $m${}^{2}_{ee}$ = $0.00242$ $\pm0.00011$ eV${}^{2}$. Assuming the normal (inverted) ordering, the fitted $\Delta $m${}^{2}_{32}$ = $0.00237$ $\pm0.00011$ ($0.00247$ $\pm0.00011$) eV${}^{2}$. Superseded by AN 2017A.

^{10}
ABE 2014 results are based on ${{\mathit \nu}_{{\mu}}}$ disappearance using threeneutrino oscillation fit. The confidence intervals are derived from one dimensional profiled likelihoods. In ABE 2014 the inverted mass ordering result is reported as $\Delta $m${}^{2}_{13}$ = $0.00248$ $\pm0.00010$ eV${}^{2}$ which we converted to $\Delta $m${}^{2}_{32}$ by adding PDG 2014 value of $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{5}$ eV${}^{2}$. Superseded by ABE 2017C.

^{11}
AN 2014 uses six identical detectors, with three placed near the reactor cores (fluxweighted baselines of 512 and 561 m) and the remaining three at the far hall (at the flux averaged distance of 1579 m from all six reactor cores) to determine prompt energy spectra and derive $\Delta $m${}^{2}_{ee}$ = $0.00259$ ${}^{+.00019}_{.00020}$ eV${}^{2}$. Assuming the normal (inverted) ordering, the fitted $\Delta $m${}^{2}_{32}$ = $0.00254$ ${}^{+.00019}_{.00020}$ ($0.00264$ ${}^{+.00019}_{.00020}$) eV${}^{2}$. Superseded by AN 2015 .

^{12}
FORERO 2014 performs a global fit to $\Delta $m${}^{2}_{31}$ using solar, reactor, longbaseline accelerator, and atmospheric neutrino data.

^{13}
GONZALEZGARCIA 2014 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 2015 as $0.002460$ $\pm0.000046$ eV${}^{2}$ for normal and $0.002445$ ${}^{+.000047}_{.000045}$ eV${}^{2}$ for inverted mass ordering.

^{14}
The value for normal mass ordering is actually a measurement of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ which differs from $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ by a much smaller value of $\Delta {{\mathit m}^{2}}_{\mathrm {12}}$.

^{15}
AARTSEN 2013B obtained this result by a twoneutrino oscillation analysis using $20  100$ GeV muon neutrino sample from a total of 318.9 days of livetime measurement with the lowenergy subdetector DeepCore of the IceCube neutrino telescope.

^{16}
Based on the observation of 58 ${{\mathit \nu}_{{\mu}}}$ events with $205$ $\pm17$(syst) expected in the absence of neutrino oscillations. Superseded by ABE 2014 .

^{17}
ADAMSON 2013B obtained this result from ${{\mathit \nu}_{{\mu}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ disappearance using ${{\mathit \nu}_{{\mu}}}$ ($10.71 \times 10^{20}$ POT) and ${{\overline{\mathit \nu}}_{{\mu}}}$ ($3.36 \times 10^{20}$ POT) beams, and atmospheric (37.88 ktonyears) data from MINOS. The fit assumed twoflavor neutrino hypothesis and identical ${{\mathit \nu}_{{\mu}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ oscillation parameters.

^{18}
ABE 2012A obtained this result by a twoneutrino oscillation analysis. The bestfit point is $\Delta $m${}^{2}_{32}$ = $2.65 \times 10^{3}$ eV${}^{2}$.

^{19}
ADAMSON 2012 is a twoneutrino oscillation analysis using antineutrinos.

^{20}
ADAMSON 2012B obtained this result by a twoneutrino oscillation analysis of the L/E distribution using 37.9 kton$\cdot{}$yr atmospheric neutrino data with the MINOS far detector.

^{21}
The 90$\%$ singleparameter confidence interval at the best fit point is $\Delta $m${}^{2}$ = $0.0019$ $\pm0.0004$ eV${}^{2}$.

^{22}
The data are separated into pure samples of ${{\mathit \nu}}$s and ${{\overline{\mathit \nu}}}$s, and separate oscillation parameters for ${{\mathit \nu}}$s and ${{\overline{\mathit \nu}}}$s are fit to the data. The best fit point is ($\Delta $m${}^{2}$, sin$^22\theta $) = (0.0022 eV${}^{2}$, 0.99) and ($\Delta \bar m{}^{2}$, sin$^22{{\overline{\mathit \theta}}}$) = (0.0016 eV${}^{2}$, 1.00). The quoted result is taken from the 90$\%$ C.L. contour in the ($\Delta $m${}^{2}$, sin$^22\theta $) plane obtained by minimizing the four parameter loglikelihood function with respect to the other oscillation parameters.

^{23}
ADRIANMARTINEZ 2012 measured the oscillation parameters of atmospheric neutrinos with the ANTARES deep sea neutrino telescope using the data taken from 2007 to 2010 (863 days of total live time).

^{24}
ABE 2011C obtained this result by a twoneutrino oscillation analysis with separate mixing parameters between neutrinos and antineutrinos, using the SuperKamiokandeI+II+III atmospheric neutrino data. The corresponding 90$\%$ CL neutrino oscillation parameter range obtained from this analysis is $\Delta {{\mathit m}^{2}}_{\mathrm {}}$ = $1.7  3.0$ eV${}^{2}$.

^{25}
ADAMSON 2011B obtained this result by a twoneutrino oscillation analysis of antineutrinos in an antineutrino enhanced beam with $1.71 \times 10^{20}$ protons on target. This results is consistent with the neutrino measurements of ADAMSON 2011 at 2$\%$ C.L.

^{26}
ADAMSON 2011C obtains this result based on a study of antineutrinos in a neutrino beam and assumes maximal mixing in the twoflavor approximation.

^{27}
WENDELL 2010 obtained this result by a threeneutrino oscillation analysis with one mass scale dominance ($\Delta $m${}^{2}_{21}$ = 0) using the SuperKamiokandeI+II+III atmospheric neutrino data, and updates the HOSAKA 2006A result.

^{28}
ADAMSON 2006 obtained this result by a twoneutrino oscillation analysis of the L/E distribution using 4.54 kton yr atmospheric neutrino data with the MINOS far detector.

^{29}
The best fit in the physical region is for $\Delta \mathit m{}^{2}$ = $2.8 \times 10^{3}$ eV${}^{2}$.

^{30}
Supercedes ALIU 2005 .

^{31}
MICHAEL 2006 best fit is $2.74 \times 10^{3}$ eV${}^{2}$. See also ADAMSON 2008 .

^{32}
ALLISON 2005 result is based on an atmospheric neutrino observation with an exposure of 5.9 kton yr. From a twoflavor oscillation analysis the bestfit point is $\Delta \mathit m{}^{2}$ = 0.0017 eV${}^{2}$ and sin$^22 \theta $ = 0.97.

^{33}
ASHIE 2005 obtained this result by a twoneutrino oscillation analysis using 92 kton yr atmospheric neutrino data from the complete SuperKamiokande I running period. The best fit is for $\Delta $ = $2.1 \times 10^{3}$ eV${}^{2}$.

^{34}
AMBROSIO 2004 obtained this result, without using the absolute normalization of the neutrino flux, by combining the angular distribution of upward throughgoing muon tracks with ${{\mathit E}_{{\mu}}}$ $>$ 1 GeV, N$_{low}$ and N$_{high}$, and the numbers of InDown + UpStop and InUp events. Here, N$_{low}$ and N$_{high}$ are the number of events with reconstructed neutrino energies $<$ 30 GeV and $>$ 130 GeV, respectively. InDown and InUp represent events with downward and upwardgoing tracks starting inside the detector due to neutrino interactions, while UpStop represents entering upwardgoing tracks which stop in the detector. The best fit is for $\Delta \mathit m{}^{2}$ = $2.3 \times 10^{3}$ eV${}^{2}$.

^{35}
ASHIE 2004 obtained this result from the L(flight length)/E(estimated neutrino energy) distribution of ${{\mathit \nu}_{{\mu}}}$ disappearance probability, using the SuperKamiokandeI 1489 liveday atmospheric neutrino data. The best fit is for $\Delta \mathit m{}^{2}$ = $2.4 \times 10^{3}$ eV${}^{2}$.

^{36}
There are several islands of allowed region from this K2K analysis, extending to high values of $\Delta \mathit m{}^{2}$. We only include the one that overlaps atmospheric neutrino analyses. The best fit is for $\Delta \mathit m{}^{2}$ = $2.8 \times 10^{3}$ eV${}^{2}$.

^{37}
AMBROSIO 2003 obtained this result on the basis of the ratio R = N$_{low}/N_{high}$, where N$_{low}$ and N$_{high}$ are the number of upward throughgoing muon events with reconstructed neutrino energy $<$ 30 GeV and $>$ 130 GeV, respectively. The data came from the full detector run started in 1994. The method of FELDMAN 1998 is used to obtain the limits. The best fit is for $\Delta \mathit m{}^{2}$ = $2.5 \times 10^{3}$ eV${}^{2}$.

^{38}
AMBROSIO 2003 obtained this result by using the ratio R and the angular distribution of the upward throughgoing muons. R is given in the previous note and the angular distribution is reported in AMBROSIO 2001 . The method of FELDMAN 1998 is used to obtain the limits. The best fit is for $\Delta \mathit m{}^{2}$ = $2.5 \times 10^{3}$ eV${}^{2}$.

^{39}
SANCHEZ 2003 is based on an exposure of 5.9 kton yr. The result is obtained using a likelihood analysis of the neutrino L/E distribution for a selection ${{\mathit \mu}}$ flavor sample while the ${{\mathit e}}$flavor sample provides flux normalization. The method of FELDMAN 1998 is used to obtain the allowed region. The best fit is for $\Delta \mathit m{}^{2}$ = $5.2 \times 10^{3}$ eV${}^{2}$.

^{40}
AMBROSIO 2001 result is based on the angular distribution of upward throughgoing muon tracks with ${{\mathit E}_{{\mu}}}$ $>$ 1 GeV. The data came from three different detector configurations, but the statistics is largely dominated by the full detector run, from May 1994 to December 2000. The total live time, normalized to the full detector configuration is 6.17 years. The best fit is obtained outside the physical region. The method of FELDMAN 1998 is used to obtain the limits.

^{41}
AMBROSIO 2001 result is based on the angular distribution and normalization of upward throughgoing muon tracks with ${{\mathit E}_{{\mu}}}$ $>$ 1 GeV. See the previous footnote.

^{42}
FUKUDA 1999C obtained this result from a total of 537 live days of upward throughgoing muon data in SuperKamiokande between April 1996 to January 1998. With a threshold of ${{\mathit E}_{{\mu}}}$ $>$ 1.6 GeV, the observed flux is ($1.74$ $\pm0.07$ $\pm0.02$) $ \times 10^{13}$ cm${}^{2}$s${}^{1}$sr${}^{1}$. The best fit is for $\Delta \mathit m{}^{2}$ = $5.9 \times 10^{3}$ eV${}^{2}$.

^{43}
FUKUDA 1999D obtained this result from a simultaneous fitting to zenith angle distributions of upwardstopping and throughgoing muons. The flux of upwardstopping muons of minimum energy of 1.6 GeV measured between April 1996 and January 1998 is ($0.39$ $\pm0.04$ $\pm0.02$) $ \times 10^{13}$ cm${}^{2}$s${}^{1}$sr${}^{1}$. This is compared to the expected flux of ($0.73$ $\pm0.16$ (theoretical error))${\times }10^{13}$ cm${}^{2}$s${}^{1}$sr${}^{1}$. The best fit is for $\Delta \mathit m{}^{2}$ = $3.9 \times 10^{3}$ eV${}^{2}$.

^{44}
FUKUDA 1999D obtained this result from the zenith dependence of the upwardstopping/throughgoing flux ratio. The best fit is for $\Delta \mathit m{}^{2}$ = $3.1 \times 10^{3}$ eV${}^{2}$.

^{45}
FUKUDA 1998C obtained this result by an analysis of 33.0 kton yr atmospheric neutrino data. The best fit is for $\Delta \mathit m{}^{2}$ = $2.2 \times 10^{3}$ eV${}^{2}$.

^{46}
HATAKEYAMA 1998 obtained this result from a total of 2456 live days of upwardgoing muon data in Kamiokande between December 1985 and May 1995. With a threshold of ${{\mathit E}_{{\mu}}}$ $>$ 1.6 GeV, the observed flux of upward throughgoing muons is ($1.94$ $\pm0.10$ ${}^{+0.07}_{0.06}$) $ \times 10^{13}$ cm${}^{2}$s${}^{1}$sr${}^{1}$. This is compared to the expected flux of ($2.46$ $\pm0.54$ (theoretical error))${\times }10^{13}$ cm${}^{2}$s${}^{1}$sr${}^{1}$. The best fit is for $\Delta \mathit m{}^{2}$ = $2.2 \times 10^{3}$ eV${}^{2}$.

^{47}
HATAKEYAMA 1998 obtained this result from a combined analysis of Kamiokande contained events (FUKUDA 1994 ) and upward going muon events. The best fit is for $\Delta \mathit m{}^{2}$ = $13 \times 10^{3}$ eV${}^{2}$.

^{48}
FUKUDA 1994 obtained the result by a combined analysis of sub and multiGeV atmospheric neutrino events in Kamiokande. The best fit is for $\Delta \mathit m{}^{2}$ = $16 \times 10^{3}$ eV${}^{2}$.
